To start: Not a physicist, just a curious idiot. Forgive my lack of understanding if there is something fundamental I miss here.
I've seen similar questions to mine, and answers relate specifically to mathematical processes at a geometric level which is beyond me, and (also beyond me) quantum theory - rather than simple to understand physical processes - especially in relation to a higgs mechanism presuming an increasing object mass as velocity increases. The answers are confusing and not consistent with any of my understandings of physical reality (I repeat: a curious idiot :)).
The problem I have: Relativistic mass increases because speed does? The presumption this is connected to momentum and kinetic potential energy (it is potential as it doesn't ACT on anything) is really dissonant to me. There seems to be no functional mechanism for Kinetic Potential Energy to create Mass which would constrain acceleration profiles of an object in a vacuum.
Is it instead that the "mass increase" mentioned at speed approaching $c$ is consistent with the increase of photonic pressure around an object acting as a barrier to further acceleration?