What you really want to do is put out the stars sooner then, and feed all the hydrogen into the supermassive black hole at the center of the galaxy. Dump in all the mass in the galaxy and all of its satellites and everything from Andromeda and its satellites too and it will grow. Nudge Andromeda’s central black hole into orbit around ours so that they merge, etc, etc. Grow it big enough and and you can build a Birch World around it, with a surface area larger than all the planets in those galaxies put together. All of the exploration with none of the boring travel in between interesting places! You can seed it with life from every planet your civilization ever encountered and watch all those ecosystems compete and hybridize as you while away the years. How many years would you have?

While dumping matter into a black hole destroys the matter, it doesn’t destroy the mass. It just confines all of the mass in one place. Powering your Birch World is just a matter of using the Penrose process to extract energy from the black hole for the next few million trillion trillion trillion trillion trillion trillion trillion years (about 3×10¹⁰⁴ years give or take a few). The stars will only last for about a million trillion years (10²⁰ years plus or minus a bit), so this plan extends your your lifetime by a factor of a trillion trillion trillion trillion trillion trillion years.

Maximal extension perhaps, but not quite forever. Forever takes a lot more work.