i've been running an old, very rumbly, 120Y sedan diff. it's the biggest borgwarner i could find. Anyway it's been rumbling away for years, 4 or 5 of them have been behind my Mild A15.
I'm not much of a burn out man but it does cop plenty of full power launches and it's still going strong.
Even this mild A15 is still a pretty low torque kind of engine compared with larger capacity donks so most of the running gear should be pretty low stressed i reckon.

The whole point is that i reckon unless your expecting massive power/torque increases from your L20 i "reckon" you'll be OK.
My A15 only puts out just over 60HP at the rear though. Can't recall the torque figures.
Ute diffs are fairly pricey these days. Does $400 -$600 sound about right? If you can get one!
However getting a propshaft made up to join the L-series box with your diff will cost a fair bit too. If you break diffs and have to change to a ute diff later on you may have to get your shaft modified again!

Also there are the ratio aspects to think of. The ute diff will let your motor spin up fast. Good for A-series engines not destined for the freeway but your L series should have the torque to justify a lower ratio diff....like the 120Y diff in there now?

I'm interested to hear what you do.