Institute pants are the best pants.
As for PAINT if you are on pc there is probably a mod out there. If console, I doubt they will. It would be like gaining the Brotherhood paint job when you help defend the police station.
I don't think that's a good comparison. You haven't yet completely joined the Brotherhood at the police station. You're not a full member. You get it just after arriving at the Prydwen, which is when you actually become a full member. After Mankind-Redefined, you are quite clearly a very full member of the Institute. I've always found this a bit odd. You unlock the Minutemen paint job for the T-45 as soon as you decide to join the Minutemen. You get the Railroad paint for the T-51 as soon as you join the Railroad. You get the BoS paint very shortly after joining the BoS. You unlock the paint jobs and will in all likelihood end up siding against one of them. Yet the only way to get the Institute paint job is by going all out and absolutely committing to them all the way through to the end.
I've only ever sided with the Institute by going back to a save and completing the quests, and I've never 'actually' sided with them and continued with that save after finishing it. I'm on a second character now, and won't be siding with them this time either. I'd love to have the paint job though. I'm headed to bed now, but tomorrow I think I'm going to track down a way to unlock it through the console.
Okay, that didn't take long. This will obviously only help if you're on PC, but here's the console command to unlock the Institute paint job. I just tried it in my second play through, which is still aligned with all four factions.
set pa_global_material_institute to 1
Then you can just add the paint job in the power armor station like any other paint job.