"Just need to borrow the particle physicist's budget for a second."
I don't think thats enough and I also don't think the market for Helium-3 is that lucrative, since comercial fusion is for some reasons still not in sight.
Apollo took 9 years and about $25 billion to get there, so we can treat that as an upper limit. However, the Capstop cubesat just reached the moon[0] for $30 million[1] so the roughly $5 Billion for the LHC should be enough to get us to the moon these days. And there's plenty of aluminum and titanium to bring back until commercial fusion arrives.
[0] https://www.space.com/nasa-capstone-cubesat-arrives-moon
[1] https://spaceflightnow.com/2022/06/28/capstone-cubesat-launc....