C4 auto trans problem

1968 Mustang, 6 banger, C4 trans. Have a problem that just recently started, only had the car on the road a few days after 3 weeks of getting it road ready.

Transmission will now only shift into 3rd gear after it has been driven about 5 miles or warmed up and then driven a few miles first.

The passing gear linkage is set correct, also added prior, a new neutral safety switch.

Just added a new trans filter, the old one was good and clean when pulled but magnets (3) where loaded with minutte metal filings. Cleaned magnets, added more as well.

Added a new modulator valve.

Noticed the other day when trouble shooting that while running, in park warmed up, trans fluid was slightly foamy, filled w/ air bubbles.

This may be important and part of the problem, when I pulled the pan I found a very small sized, what looks like a washer but has a long slot in it, rounded in the center of the slot (entire piece is smaller than a dime), could not locate anything that it could have fallen off of but it was night and using flash light w/ other lighting. Found it near the rear of the pan.

Refilled with fluid, test drove and still same problem and symptoms, tested shifter linkage while driving and slowly slid lever up toward neutral, went into neutral where it should have so believe linkage is correct as well, once warmed up and a few miles on it, it shifts perfect every stop and start, any suggestions?

QUESTIONS?
How would I adjust the bands and which screw is it for 3rd gear, the nearest to the bell housing or the one near the back of the trans? (the ones near the linkage hookup)
Could the modulator valve be adjusted as well, turned in or backed out?, how much each try, 1/2, 1/4 turn? Thanks for any replies, I know this can be a tough one.

Thanks for the answers, I'll give the K&N a try, I've heard these additives swell the gaskets etc... so that kinda seems like a solution to try to both your answers.

Still curious what the small washer deal goes to that I found in the pan, this car is fighting me every step of the way. Have the power steering problems as well after rebuilding (most) of the front end but won't even get into that right now.

Finally worked out the charging system problems so I know the car isn't cursed like I was beginning to think it was,lol.
Will be checking back for other answers or suggestions daily this week.

Brianj5600, my camera broke last week so can't get a pic and haven't been able to find any similar part on a web search. The center of it is not as rounded as I first thought, just very slight. Also it seems to have a backing on it.

I'm gonna run out soon to a trans. shop and ask them what the part may be and will post later what they had to say and if it is even related to the symptoms.

The trans. shop told me today the small metal washer was a retainer that came off of the dipstick top and wound up in the pan. So no loose or fallen out parts in the pan at least from the tranny.

CraigMBA: I don't know if anyone else ever had the pan off, I assume yes because the old screen was clean as new when I had it off, inside pan was clean but magnets (3) were loaded w/ filings. Odometer reads 80K but doesn't work at present so no idea what actual mileage is.
I'm going to try a quart of K&W I picked up last night and plan on a rebuild over the winter regardless if the K&W works or not.

Re:Soaring1, OK, will give that a try if problem persists.

Problem seems solved

OK, did the K&W trans. fix I bought at Advance Auto yesterday, ran car a good 30 miles after putting it in and ran it hard a few miles once it was warmed up and going into 3rd gear.
Let it cool about 4 hours and took it out again, some improvement, shifted into third after only about a mile.

Took it out today after setting since last night and now it shifts into 3rd gear with out having to be warmed up, 1st and 2nd shift very solid as they did, going into 3rd is more of a slight "ease" but it goes into 3rd fully now. I can't believe I got out of this for only $8.00 plus a few trans fluids (for now anyway), I needed a break.

Re: Soaring1, will check into the intermediate band eventually also.
Thanks to all that contributed to this question. J