Price would be typical to getting your engine refreshed and then getting a Harrop HTV
The LSA crate is over $20k to start with, then you need all the auxiliaries for the little 1900 blower
Rebuilding your LS can be had for under less than $10k with cnc heads, cam, springs, Cr rods and trunnion upgrade
https://www.lsxperformanceparts.com.au/ls3-6-2l-reconditioned-engine-with-cam-package-long-motor/⁹
A HTV 2300 or 2650 can be had for about $13k with everything you need
For me, the ability to remove the supercharger for resale later down the track is handy as you can just remove the blower and replace your intake
Plus less logistics involved with needing to change engine numbers, rego, insurance
Plus there isn't really anything special inside the LSA, apart from having a little blower on top
The only benefit for a LSA crate would be having the ability to gather parts, thus minimising the time the car will be off the road
Engine rebuild can take weeks at a minimum, when you can book it in, to months (contact your engine builder for accurate build time)
I would rebuild, put a 2300 on it and let the good times roll, it will cost typical to sticking in a LSA, but will be so much better
I would also look at factoring in getting the transmission rebuilt and a big transcooler if it's a 6L80E, or a good clutch upgrade if it's a TR6060
https://www.craigsautos.com.au/automatic-transmission/performance-cars/
Have fun, start a build thread