Both of those issues are reasonable, Sherlock.
To take the first one, that Republic reinforcements may be en-route during the Starkiller battle, that is actually what I imagine happening at this point. In fact, my concept is that the Raddus and its attending ships in TLJ are actually these reinforcements, they merely got to the Resistance too late to help in the Starkiller battle. This is also why the Resistance has a specialized fleet of what appear to be gravity-based, planetary bombers. This makes a lot of sense if they were being sent to take out something like an Oscillator on a giant planet Death Star, and not much sense for anything else.
I do agree that it should be unclear whether or not the ships actually launched before the system’s destruction, with the implication that they couldn’t even launch. This would make their appearance in TLJ a bit of a welcome surprise.
To the other point, here’s the idea for the new ending:
-After returning to the Resistance base and Chewie’s mourning, play the scene of BB-8 going to R2 again, this time with C-3PO discussing the backup memory.
-At the end of this scene, BB-8 looks down the hallway at Rey, who has watched this encounter. This uses a deleted scene where Rey is watching the doctors work on Finn but merely changing the context of the scene.
-Cut to night at the base, with R2 now hooked up to machines and beeping slowly as he is recharged/his memory is searched.
-R2 wakes up and the other droids join him, and the rest of the film plays out normally.
This scene serves to solve the R2 map subplot in a way that involves the main character acting in a way that is entirely natural for her, as well as giving her added reason for going practically alone in search of Luke.
Now I can see the issue with merely establishing R2 as more fanservice, and I actually do think that something more is required in the first scene other than just R2’s presence.
In thinking about this last night, I had the idea that perhaps R2 is in clear disrepair. For example, there could be panels hanging half-off of his body and he is smeared with dirt and oil. I imagine that this wouldn’t be too difficult to implement since R2 would be stationary for this change. In this state, BB-8 unveiling him is less like reuniting with an old friend and more with realizing how neglected he has become. BB-8’s sadness at seeing R2 in this state is immediately understandable and enhances the theme which is apparent in the scenes of Han and Leia happening around this point - our heroes are in a bad place and relationships that should be vibrant are stained with neglect.
Also, if R2 was so damaged, Rey’s involvement in the final scene would be much more expected since she tends to fix droids out of hand. You know, that whole “Your antenna’s bent” thing. When the scene transitions to night, R2’s broken and dirty panels are fixed and now he merely needs to wake up for the rest of the plot to happen.
JEDIT: R2 being damaged is also in line with TFA’s theme of repurposing plot beats and imagery from ANH while repurposing it for a new context.