The difficulty here is that before General relativity appeared on the scene, it was your viewpoint that was standard. So, the inertia to be overcome is the inertia represented by your view that time must be infinite.
Second, the reasons you give for your position are not even close to being sufficient. In fact, they miss the basic point if, in fact, General relativity is correct.
Third, it is very, very dangerous to think you know how the universe 'must be' if you have no actual evidence for your position. Your claim that you are confident that a way out will be found is faith based on no evidence. You may be lucky and be correct, but you may also be unlucky and be wrong.
And fourth, general relativity is not to be summarily dismissed. It has passed all the tests it has been subjected to so far. That carries more weight than your philosophical arguments, no matter how definitive you think they are.
Fifth, studies into quantum gravity are part of the current orthodoxy. String theory, Loop quantum gravity, and other possibilities are being very actively pursued. At this point, NONE of the different alternatives has been able to make a testable prediction. Well, string theory predicts the existence of gravity. So *all* of them have to be taken with a huge grain of salt.
And finally, the *only* way out of the finiteness of time is if quantum effects overwhelm the general relativistic effects. Even with quantum gravity it is possible for time to be finite into the past. So to have confidence of the sort you have seems to be a HUGE over-reach of your reasoning.
I would suggest you might want to reconsider your dismissal of the possibility of finite time and ask why it follows so naturally from what we do know.