I agree with Richard that the best way to go is to remove all glue if
possible. 

Personally I had the impression that the Titelock 3090 will glue quite well,
even if not all glue could be removed, it's nasty stuff and hardens within 2
minutes so you have to work (very) fast. It's really something to use for
the desperate cases and not at all for normal work. Anyway you could always
test it by applying e.g. Titebond to some scrap wood, let it dry completely
and then without removing the glue try to glue them together with Titelock
or a similar kind of glue and see what happens.

If you use screws from the outside it won't look pretty. You could of course
remove the screws once the glue has completely set and then plug them. By
preference use a small diameter hole cutter so that you don't end up with
end grain in your plugs. The end grain will show when you restore the
paintwork.
If you very lucky, then the bottom is only screwed on but in most cases this
is wishful thinking :-(

Good luck!

Chris.

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