Get a factory service manual - detailed step by step. Skim it and ask any questions.
2003 transmissions (even H6's) are exactly the same are removing the 4EAT from my 1980's XT6's.
There's almost no appreciable difference at all - exhaust, mounts, bellhousing bolts, TC bolts, starter, driveshaft, CV's.
Main tricky parts are: 1. rusty exhaust bolts - the exhaust manifolds - make sure you use 6 point sockets and don't strip the nuts. Or be prepared to cut them off with a dremel. Converter flange bolts - they'll shear off or cut them.
2. tilting the engine/transmission so the trans comes out - the bellhousing will want to hit the transmission tunnel of the chassis without sufficient angle pulling off the lower end studs.
front of engine needs pushed up so the rear of the trans will rotate down and angle out without the fat bellhousing hitting the trans tunnel.
only tricky because there's no set measurements, it's not hard in and of itself.
if you've pulled an engine/trans before - then you already know/get this.
1. drain gear oil and ATF from trans and disconnect ATF lines at trans (ATF will want to pour out when you pull the driveshaft out the rear).
2. remove front wheels, inner CV roll pins, top strut mount bolts (mark head location for reinstall/alignment), and loosen the lower strut mount bolt so you can pull on steering knuckle to pull axle off trans stub
(no need to remove the axle or axle nut)
3. remove exhaust under trans
4. remove bellhousing bolts, pitch stopper (dogbone), and starter, disconnect transmission electrical connector.
(pulling axles first gives easier access to those lower annoying 14mm nuts
*Make sure you get all the bolts - look on the donor trans for each bolt location and verify you removed it - it's easy to miss one on these "8 bolt" bellhousings.
5. remove engine mount nuts - 14mm
6. support trans (floor jack, straps, chain through engine bay) - and remove trans mounts
7. disconnect neutral safety switch cable/connector - the shifting mechanism on the passengers side front of the trans and the rear O2 sensor - i think it connects to the rear passengers side of the trans if it's still attached.
8. tilt trans back and pull it out.