Paul, I may take you up with the new tip. The rest looks like a fun job for me. On second look, the cue is whole, it just is not lining up correctly and for some reason, I did not see the corresponding grain patterns.
If things work out to my satisfaction, maybe I'll send both halves and once the new tip is attached, you can take the cue out for a test game or two

.
Oh, I have to weigh it, but I think it is on the heavier side.
Dave