It is immediately reconciled at low speeds. There is no need to go to quantum gravity whatsoever. We have a theory we trust at all speeds (not all scales), namely general relativity which reduces locally to special relativity (SR). On the other side we have quantum mechanics where we speak about small things, at low speeds, which uses a Newtonian notion of time as absolute, in other words there is always a laboratory frame where time flows.

The reason why time must become a part of space-time at higher speeds has to do with (the speed of light being the same in all frames) the specific form of the Lorentz transformations, which mixes space with time. If you take the limit of low speeds you will be able to neglect such term and therefore conclude that all frames will share the same time coordinate. You obtain then equations which are again symmetric under Galilean transformations and thus time becomes absolute again to all observers.

To sum up, at low speeds time becomes again absolute, meaning it is not mixed in a complicated way with space components and allowing all frames to share the same time variable. This in turn means your equations will reduce properly to those treating time as an external parameter.

It is immediately reconciled at low speeds. There is no need to go to quantum gravity whatsoever and also not even to quantum mechanics. If you check how time is understood in classical mechanics, you already can convince yourself that time in such regime is absolute, thus I believe you are trying to understand this difference. You can then later go to QM mechanics without change since the relevant parameter here is speed, not sizes. 

We have a theory we trust at all speeds (not all scales), namely general relativity which reduces locally to special relativity (SR). On the other side we have (classical or quantum) mechanics where we speak about lower speeds, where we use a Newtonian notion of time (absolute), in other words there is always a laboratory frame where time flows.

The reason why time must become a part of space-time at higher speeds has to do with (the speed of light being the same in all frames) the specific form of the Lorentz transformations, which mixes space with time. If you take the limit of low speeds you will be able to neglect such term and therefore conclude that all frames will share the same time coordinate. You obtain then equations which are again symmetric under Galilean transformations and thus time becomes absolute again to all observers.

To sum up, at low speeds time becomes again absolute, meaning it is not mixed in a complicated way with space components and allowing all frames to share the same time variable. This in turn means your equations will reduce properly to those treating time as an external parameter.