Update! A friend and I did this trip recently:
When I checked the gauge for the Gila Wilderness section the day before we got on the river (April 3rd) it was at 390 cfs. At this level we experienced no rapids above class II. There was a lot of maneuvering because of the low water level, but if you messed up and flipped you could basically just stand up in most sections or have a very casual swim to shore. I can definitely see how there would be some class III rapids and strainer problems at higher levels. I would not recommend bringing a raft with the river at the level we floated it on. The packrafts were fine though. We scraped the bottom a few times and a couple times had to get out of the boat, but overall very enjoyable. It was a beautiful float with great views and I would highly recommend it!
1st day: Put in at around 10:30 am and floated until about 5:30. Took a few breaks in between and never pushed ourselves. Went about 17 miles.
2nd day: Put in around 11, multiple breaks. Stopped around 5. Went about 12 miles. Another easy day.
3rd day: Put in around 10:30 again, no breaks, went about 6 miles and took out a little past where Turkey Creek flows into the Gila at 12:30. There is a trail that crosses the river there, but it may be hard to spot if you are not looking out for it. We had lunch, packed everything up and hiked up Turkey Creek to the hot springs and camped the night there. It's only a few miles or so up the creek to get to the springs which are awesome. On the hike up the creek you'll get to a pool of water with a little waterfall. There's a big boulder on the left hand side with a hole. You'll have to take your backpack off and drag it/push it while you crawl through. A little farther past that are the hot springs. There are multiple small pools, just search around the sides of the creek.
4th day: We did not get started until about 11 am. We decided we should hike up turkey creek until it met up with the trail, but that turned out to be too difficult. It was very slow going up the creek and I had to take my backpack off a few times and hand it up to my friend to climb up a few of the boulders. So we decided to cut up the hill and hoped we'd hit the trail. At first it was steep bush whacking and then it turned into a scree field. We did eventually hit the trail after gaining about 500 feet. Trail was nice for a couple miles until we got back to the creek. Then it started to be very overgrown and slow going. Our arms were very scratched up from pushing through so many branches. We lost the trail a couple times, but it's not a big deal since you're following a creek the whole time. Eventually we hit a sign by some switchbacks saying Miller Spring was 2.5 miles away. I think the trail between this point and Miller spring is actually a little bit off on caltopo. But it is easy to follow. Just be aware if you are using a GPS it might not line up. Do not bother filling up much water from the creek since there is a perennial water source at Miller Spring. There is a cabin there, but it's locked because of "misuse." So we camped outside by the fire pit. This was a hard day for us even though it was only 12 miles. We didn't finish until about 7:45 pm and were pretty sore.
5th day: left at about 10:30. Followed the trail going north (there is no sign for this trail as there are for the others). There is another perennial water source before your next intersection. There is a sign at that intersection and you'll want to go the direction of "little creek." You'll cross a few creeks on your way down to the parking lot, so you don't need to fill your water up too much. The trails were very easy this day, but we were pretty tired from the previous day. When we finally got down to the parking lot at about 5 pm or so, we went to the bridge, inflated our rafts, and floated back down to where we parked our car. This section of the west fork was VERY low. Barely boatable.
We had our car parked at the campground by the bridge and just left a note saying how long we'd be gone for on the dash. No price for parking or camping there. Was very convenient! If I was to change anything, I would have started earlier the 4th day or would have made it 3 days walking back instead of 2 to make it a more pleasant trip. Hope this helps! I thought I'd add a detailed account since I couldn't find many myself online.