The best substitute, in my opinion, would be a 18 or 20 inch Roto Tom.

If you can't get a hold of a Roto Tom that big, I would try anything that does NOT have a resonant (bottom) head. If you are going to use a Floor Tom, take the bottom head off; it will sound closer to a Timpani.

Timbales might work as well, such as the low drum. You've already got the single head happening, plus the brass shell (if you have brass timbales) my assist in creating the copper bowl ring you get from Timpani.

I don't know how far out you are trying to get sound wise, but it sounds like you've got a lot of good ideas.

You could even try using a Kick Drum. Play it horizontally without the front/resonant head ... and use single-ply head on the batter side if you've got one. This will allow more resonance and high frequencies than if you use a two-ply head.

If you used the pitch modulation, a djembe or djun djun might be cool ... using soft mallets, and tuning the drums down.

The sky is your limit I guess.

Great ideas, Bart!

If I need the tympani sound on my next song (I think I might), I'm gonna try out the kick and tom ideas.

I agree with Bart's suggestion that roto toms will be the "next best thing."  If you can't get access to roto toms, tho...

If you want to have a definite pitch, not just the timbre of timpani, use a floor tom or bass drum as has been suggested already, and try recording the pitch(es) you want, played on bass, and mix in the bass track just enough to give that sense of pitch to the sound.  This won't work for heavy-duty "Rite Of Spring" timpani parts, obviously, but for a single note, or maybe two, it might help to sell the effect a little bit better.

In college we played pieces that required the use of impact bass drums.  These are quite similiar to a tymp. sound, without the definite pitch.  I think you should use bart's suggestion of using a kick drum(assuming you don't have access to a big ass roto-tom!).  

First, you only need one head, a thin "ambassador or G1 type head, clear, lightly coated, suede, or renaisance, whatever you prefer).  Tune it pretty low.  Now place the drum on some sort of stand.   You can use chairs for this, whatever works, improvise dude!    I would think it should be placed horizontally, but could work vertically with proper mic placement(plus vertically would be easier to mount and play).  BTW, you won't acheive the true sound of a tympani using drumstics!  Make sure to get some mallets(although you won't need the professional ones.  Just get the Saul Goodmans, or the Vic Firths)