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The 2ZZ-GE does have a shorter stroke, but it also has a way higher compression ratio and very low lift on the low cams. The efficiency should be just as good if not better than the 1ZZ.
The U250E goes on 2AZ-FE equipped engines. Totally different, won't fit. Also keep in mind, those automatics are very prone to unlocking.
For max fuel economy, the best you can do is 0.725 top gear + 3.9 differential for around 2500rpm at 60mph. You can try oversize tires but that might be bad for aero. The 1ZZ might be able to pull a Matrix along at 2000rpm, but below 2000rpm it's basically useless. In my MR2 Spyder, the 1ZZ would make a loud groan at 1400rpm and basically zero power if it was in 5th. By 2000rpm it would be moving along if I had the pedal floored. I'd drop the rpms no more than 2400, because the Matrix is much taller and heavier, unless you plan on cruising at higher speeds. At 2000rpm you'd probably be running over 70% load which is efficient, but a slight grade and you'll be downshifting.
I believe the usual automatics that came with 1ZZ Corollas were 4 speeds with a super tall 4th gear that did run at 2000rpm, but the engine immediately would spin to 3500 if you needed more power.
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