Cut the crossmember and weld on the Galant brackets for the engine mounts. The flex plates have different mounting holes so you'll need the one from the Galant. Only the Galant transmission will bolt to the flex plate and engine. You'll have to use the two half shafts from the Galant. The shafts will have to be cut in half, then have some metal added to extend them. Their outer cv joints don't match the wheel bearings, so you'll need the entire strut / hub / bearing assemblies. The upper strut mounts will not fit inside the strut towers so something will have to be modified and welded.
The 3.8L wiring harnesses and connectors are different. You'll need the Galant's Engine Computer to run the injectors. The Engine Computer will not communicate with the Body Computer, Air Bag Computer, and Anti-Lock Brake Computer if you have that option. The Body Computer also talks to the instrument cluster, so you'll have to replace the dash too.
If the Galant engine needs higher fuel pressure, you will have to use it's fuel pump. The pump will only mount in the Galant fuel tank. If the fuel filler tube is on the driver's side, you'll have to mount the tank backwards.
OK, by now you figured out it won't work. Half of those differences even pertain to swapping your 3.0L Mitsubishi engine for Chrysler's 3.3L. Both were available in the Dynasty. I have a '93 Dynasty with the 3.3L and two Caravans with the 3.0L. It is not even practical to put the 3.3L in your car.
You should have no trouble finding a good 3.0L in the salvage yards. I have a freshly rebuilt one waiting to go into one of my high mileage vans when necessary. You didn't mention what's wrong with your engine. The most common failure is the lower end, (spun rod bearings and a chewed up crankshaft). For a total rebuild, parts for mine cost less than $300.00 for a remanufactured crankshaft, bearings, gasket set, and separate rear main seal. Students took care of the labor. If that sounds like it's what you need, you might consider looking for a local community college with an Automotive program. Very often they need live work for their students, and they usually do good work.