On a side note, there are no AWD 4G63 engines.
There are however, 4G63T engines with AWD capability.
Here's my 12 years of DSM tuning knowledge... Get ready for some school.
A 4G63T will fit in the engine bay. You will need an engine from a 1G or 2G Eclipse GS-T. I recommend the 1G engine as the 6-bolt is way better than the crappy 2G 7-bolt. It is NOT similar in any way other than it's a I4. $7,000 is pushing it for this particular engine swap. The engine has to be mounted to the other side of the bay to get it to work.
How do I know? I've done it to a 2002 Eclipse, which does have a stock engine like the TIburon and mounts at the same points. The following picture is what the swap looks like when completed.
(2002 Eclipse with a 4G63T swap. Fully built block, ported, polished, cyro-treated parts. 32psi. 546whp.)
(Notice how the engine is now on the right side...)
The entire K-member and new mounting points had to be made. Custom axles, cv-joints and the works had to be found/made as the engine had to be mounted different changing all the clearance specs.
To put a built 1G DSM 4G63T into a 3G DSM that had a 4G64, cost with custom parts manufacture labor, was just under $10,000. If you do without all the bells and whistles of a fully built engine, I would guess about $8,000.
So, your shop is not too far off for a FWD to FWD swap. No way AWD is going to happen.
But what do I know, I'm a girl.