Owning your own home

Should I point out to the EA that this other interested party likely has heard all about the tens of thousands of pounds of work needing doing direct from said builder, and may even already have a copy of the survey we had done, as we gave the builder a copy?

No. Keep it professional. You need them to not dislike you. They will see this as underhand.

And should I casually mention this to the EA today to see if it rattles them a bit?

It's pie in the sky until you've had an offer accepted on it, I can't imagine it will affect their way of thinking, even if its through a different agent. If you were viewing it, and had put an offer in on it, then that will change.

Also, get viewings on the other house, it sounds better than the one you are trying to buy! Who wants a place without a downstairs loo FFS!