Do you have any photos of the existing 10.0 legal cage? A 10.0 cage MIGHT be able to be upgraded to a 8.50 if the bars are in the right spot, but MRC makes the pre bent kit these days that's actually nice and an easy weld in.
The issue is a chassis shop (since you mention you aren't a welder) is going to probably charge more to upgrade a decent 10.0 cage rather then just buying a new good quality 8.50 kit and starting from scratch. If you are in the central, east, or south in the US there is likely a chassis shop that can put a pre bent cage in under week for ~$2500. I'd expect a pre bent kit to be $5000 installed and NHRA inspected. There are additional things like battery cutoffs, bellhousing/trans blankets, driveshaft hoops, harnesses, etc that aren't included in there.
Low 9's is a serious car. If the 10.0 cage is well done, you could likely look at just getting some instant center improvement bolt on or light weld on brackets and going from there. If the cage is OK possibly pull some timing out, try to get it to run 10.0's reliably. The jump from 10.10 to 9.70 is significant in terms of safety equipment so I'd get the car to be reliable 10.10 first, and then look at going into the low 9's.
I totally get the staged, budget build. The issue is when you jump into a car that already is a serious high HP setup it's tough to grow with the power as it's already there. You have a lot of deferred chassis/safety mainentence.