Quite a few guys run stage 2.5 ported heads on an LS1 or 5.3 for that matter with good results. I think you can get a nice running engine reaching the numbers you want using more of a stock bore and use stock parts for way less money, just the savings in heads alone is quite a bit.
Here is a link on a set of those heads,
https://www.texas-speed.com/p-4345-p...-outright.aspx
That link is for an outright set of heads, if your heads are decent enough you could send them in to save even more money if you wanted to.
Just an idea, not sure if you saw anything about this type of option.