"So, not having a plastic welder (cost nearly $300 U.S.), I wonder if there is an alternative.  
The tank is polyethylene or polypropylene, right?  Are there plastic weld chemicals that will 
work?  Or cements?" 

Until I found out my friend had the welder, I was going to use what I've used on almost
everything else, and that's Loctite Black Contact Adhesive. As a matter of fact, I'm
betting it would do just as good a job as the welder did. Easy to "tack" the inverted
top piece on, let it dry some, then fill in open spaces along the joining surfaces.
As far as effectiveness, I don't think there would be any difference.

The thing I liked about the welder is that when we cut the top section off, we left
"tabs" on the cut-off piece, so we could bend them over to anchor that "lid" onto
the tank. The welder melted those onto the lower tank nicely and after we were
done, you couldn't tell where they were. Not that being able to see the tabs would
affect the function or effectiveness of the "lid".

Dremeling that section off, keeping the cuts straight, probably served the welding
that back on more than the welder did. It was easy to put that section back on
because the cuts were so straight and precise, making the gap between the tank
and "lid" small and easy to fill in.

The Loctite adhesive dries to a rock hard finish over a 24 hour period, so it adds
a stable finish to anything it's used on.

bob