If contemplating and reflecting upon deep subtle questions and issues are what interest you, I suggest majoring in physics and minoring in philosophy as an undergraduate, or vice versa. Then, for graduate school, go to the philosophy department and specialize in the philosophy of physics.
The average theoretical physicist hates contemplation and reflection. Should you choose to become a theoretical physicist anyway with a contemplating as opposed to a calculating attitude, expect to be rejected for jobs, face active hostility from your colleagues on a regular basis, have your grant proposals rejected, have your articles go uncited and be denied tenure, if you even make it that far. Expect to spend most of your time working on minor technical projects performing tedious repetitive calculations which are pages long, and oftentimes leave you with little or no further conceptual insights at the end of the day. You might have the technical ability to perform these formal symbol pushing calculations, but your heart might not be into it. And you will regularly run into colleagues who think these formal symbol manipulations and equations are the same thing as physical reality itself, and would like nothing better than to "shut up and calculate". For them, "understanding" means nothing more than knowing which equations to use, and how to calculate. They won't see these symbols as a mere facade hiding a deeper reality behind them. They care about "how", but not "why".
It's mostly doing stuff as opposed to contemplation.
is a very telling description of your personality. Let me tell you one thing. Much of theoretical physics is just like engineering in this respect. On the other hand, philosophers contemplate a lot, but do very little or no stuff apart from publishing and giving talks on their contemplations. They seek to truly understand reality at deeper and deeper levels, and are not content with superficial understanding. They are also compelled to unearth and correct any possible misunderstandings they might harbor, no matter how the truth finally turns out to be.
Don't get intimidated by the job prospects in philosophy, because if you choose to persist in your contemplating ways anyway, you're likely to get kicked out of the leaky theoretical physics pipeline.
Should you choose to become a theoretical physicist anyway, consider cosmology, quantum information/foundations, quantum gravity or complexity/chaos theory. These fields are a lot more accepting of contemplating types, or more accurately, contemplating types gravitate toward these fields. Once again, fear not the job prospects in these socially marginalized fields because in case you choose to join some other field, trust me, it's likely you'd be spat out by the system in due time for being a poor cultural fit unless you hide your contemplative nature and treat contemplation as a shameful private indulgence which can only be pursued furtively at nights and during the weekends, and around others, you put up a respectable front and pretend you don't do such things and never talk about it. There are very few contemplating types among AMO or condensed matter physicists. Most people in particle physics tend to skew toward anti-contemplation as well.
See the question What is the difference between a philosopher of science and a theoretical physicist?
If you don't trust me or think I'm exaggerating, go ahead and ask other contemplative types.
PS: If you're a "calculator" and not a "contemplator", then philosophy was not meant to be for you. She's not your right partner. Embrace string theory instead. There's just so much calculating to do with her: plenty of loop integrals, plenty of differential equations to solve and all the beautiful mathematical gadgets of complex analysis, differential geometry, differential topology, algebraic geometry, Calabi-Yau manifolds and so on. You can easily fill up stacks of papers and notepads with your lovely calculations for days or weeks in a row in an enraptured trance. You will find yourself surrounded by a community of like-minded admirers, and you will make such a good fit into the string theory fan club.
String theory is just so beautiful and elegant! She has so much perfect symmetry from every perspective! There's just a duality or plurality about her, with her well proportioned form, so that she looks so different from every angle, but yet so stunning in all directions. You will be smitten and fall in love with her. And she's just so unique too! No one else can match her beauty! And such perfection! She's just so perfect in every way that making even the slightest change to her in any way would turn her into an inconsistent mess. And she's so tantalizingly mysterious that you just can't wait to uncover more and more pretty aspects of her. Her incomparable elegance is enough to make you feel she is the real thing, because you can just feel her realness strongly in your heart beyond reason. Not that you can't easily come up with a long list of reasons to justify her from deep within your heart. Such beauty just has to be for real because how can such beauty be faked? And something so stunningly beautiful just has to be manifested in the real world because you just know — without any need for reason — that this world is beautiful at heart.
The stacks of paper are your canvas, and the differential equations and mathematical gadgets are your pallette. There's no need to inquire about the nature of the pallette and the paint; they're just tools, albeit beautiful ones (but try not to think what they're ultimately made up of; $\epsilon$-$\delta$'s, equivalence class of atlases of arbitrary coordinate charts? ugh! What pollution of beauty!). Your pen is your brush, and with it, you will dance around painting such beautiful equations as you make manifest a calculational portrait of your true love on canvas. Your calculations are a work of art revealing her beauty to yourself and others.
You won't be contemplating or reflecting. No, no, no! You'd be gazing admiringly and savoring such lovely portraits of your true love for hours. You'd be so grateful you can play and dance with her everyday. You just can't get enough of her. You'd be compelled to produce more and more portraits of her, and devouring more and more portraits of her by fellow painters. Each portrait will reveal a different side of her.
Why should you care about her deep interior reality behind her surface? She's already so pretty on the outside. You just want to admire her beauty, and savor her mysteriousness. And deep deep down, you don't really want to understand her because that would just take away the aura of mystery surrounding her. And deep deep down, you're also haunted by the nagging fear she might not actually be so pretty at deeper levels. That's why you will vehemently attack anyone who dares to try to analyze her philosophically. After all, you are only defending her beauty and mysteriousness from anyone who dares to try to deconstruct them.