I hope that much damage was done by removing the seal after install.
If not... I have a few thoughts. Anything I say at this point... is not meant to insult your intelligence,,, But me just "checking off all the boxes" since I don't know how much experience you have.
First... I assume you checked the "slip fit" of the seal on the back of the balancer,,, to make sure the seal wasn't too snug? It shouldn't be a force fit,,, but instead slide on freely with a slight resistance.
Second... The black, (flat side), of the seal was installed facing the balancer?
Third... if you didn't use some sort of tool to install the seal,,, but instead tapped the seal in around, (circular manner), the crankshaft snout with a hammer,,, this can sometimes tweak/twist a seal enough to oval/egg the inner diameter of the seal enough to damage the seal and "catch" when installing the balancer.
Fourth... sometimes seals need a little "glue" to hold them in place. Indian Head cement, (shellac), or something similar might help, (allowing for dry time). Also... a little "assembly lube", or oil... or grease on the inner lip of the seal reduces friction. Most seals aren't installed "dry".
Fifth... I haven't yet had the priviledge of pulling the front cover on my LS... but if it doesn't use dowel pins for alignment, (or there is some slop between them and the front cover),,, the hole for the seal may not be concentric with the snout of the crankshaft. Keep in mind that even 1/32 of an inch, (a little over 30 thousandths), .031+, could be enough to catch and bind on the edge of the seal while installing the balancer.
Not knowing any details... my best guess would be #3 or #5.
So I bought a new seal and tried putting this one on the balancer then installing the balancer, but it won't seat fully in the timing cover.
This is because there is a "step" on the crankshaft... preventing the balancer from going back too far... plus the back of the balancer isn't meant to run right up against the face of the seal.
Hope this helps... and that I haven't insulted you.