Surely, given a century, our scientists will figure out something.
When ever I hear that, the optimist in me wants it to be true. The pessimist thinks otherwise and nowadays the pessimist usually wins.
We will have hotels in orbit by the 1970's - they will think of something! That was a legitimate thing that the Hiltons proposed back in the 1960's.
Your example of hotels in orbit is an incorrect example. If humanity wanted to build a hotel in orbit, we would have a hotel in space (we already have a crappy hotel - ISS). I don't consider Hilton's incompetence to represent humanity's incompetence.
When it comes to material shortages, fusion power, limits of computer chip scaling, global warming, over fishing, plastic waste, hyper effective battery storage, nuclear deescalation etc... have all been answered a lot with - they will think of something. Yes, there have been improvements but with most of these things, we have also missed the mark by a long shot. And decades later, we haven't. Sometimes it is right, look at what we did with CFC's. But it is by no means something I would hitch my wagon to.
John Michael Greer calls phrases like these 'Thought-stoppers' Little saying that we have that mean we don't have to face the ugly truth of something or are just trying to be a little too optimistic about the future in the face of hard times. "Housing prices only go up", "They will think of something", "Stock prices only go up", "It is different this time", "The fundamentals don't matter any more" etc.
There would be very little left of a vehicle after being blasted by relativistic hydrogen nuclei for 3M years on its way to Andromeda. And, who would be listening for its report 6M years later, if it could get to Andromeda intact? Or even 500,000 years later, from one of the Magellanic Clouds?
It would make sense to gather up your whole civilization and set out at a statelier pace, perpendicular to the galactic plane, to get clear of the numerous hazards that all threaten to sterilize your whole solar system when you are in the thick of a galaxy. Then it wouldn't matter if it took a million years to get clear. Probably you induce a polar jet from the sun for propulsion, and bring the whole solar system with you. (You would leave the Oort cloud behind, sadly.)
If not, then we can use a galaxy's resources to slow us down. Basically a complex version of planetary-slingshot.
My argument is, given a century, we are likely to be able to find some way to decelerate. Consider our accomplishments in the last century (airflight, spaceflight, computers, nuclear, internet)