Car: 1966 Chrysler 300 383/4bbl all original w/ 120k miles on it.

I had a leak in my transmission pan gasket and the fluid level dropped to somewhere below the dipstick during a long highway roadtrip ( I was on the throttle hard for most of the way)

Went to drive it today and it was incredibly slow to shift into D, and would spin the engine w/ no forward motion. Checked the dipstick, and after tightening the trans pan bolts, filled the level back up to normal. The fluid on the dipstick is an icky brown color - now the trans will slowly shift into D but is slipping badly, and will just spin if I give it any power at all. Upshifts are not noticeable at all, and it won't take any power at all. Before yesterday upshifts were nice and firm and timely.

Could I have damaged the trans or do you guys think I can just change out the fluid and carry on?

I was thinking I could disconnect the trans cooler line at the radiator and let it idle in N while it drains into a pan and I pour fresh fluid in through the dipstick tube?