You probably have this all researched out by now, but, or you're trying to get back to Oregon via 395 . . .
Are you doing the JMT? . . . I've thumbed from the Portal to LP a bunch of times and it's never a problem. Funny enough, there's usually about twenty fat guys in humongous EMPTY trucks that'll pass you by, before some little old lady in a beat up toyota with no room and a dog (my ride last summer) will pick you up.
if you've got the time, make a call from the portal to the Dow Villa and reserve a room––I call them the backpacker specials and I don't know why they don't but . . . $50-55 bucks this summer probably for a room/2 beds with shower and toilet down the hall. CLEAN place. Best hot tub in all of LP. (although I did get a whiff that Doug, here, or someone is opening a hostel next to the Dow. Is it finished yet?)
I've also never had a problem getting out of LP. Of the eight times I've been out of there, I've only taken the local shuttle once, but that only gets you to Bishop.
And only once have I ever had to spend a night in Mammoth and take the 7 a.m. YARTS shuttle into Y-valley. it gets you down there by about 1pm––long enough to dawdle around and wait for afternoon YARTS/AMTRAK bus to Manteca or Modesto (depending on rock slides and so on, or not) which leaves around 330pm.
Usually, I leave LP, NLT 9a.m. and I am at least at the 120/395 junction by three––usually after wandering around Bishop for whatever . . . muffins, sandals . . . again, if you're not in a hurry, you'll get that ride to T'me or even the valley and then just stay in the backpackers campground until the next valley shuttle in the morning.
My biggest tip––if you are successful in thumbing a ride OUT of the valley and you are headed for the AMTRAK, GO TO MANTECA.
I met some great guys who offered to drop me in Manteca or Stockton and I chose Stockton. Bad idea. there's a train that leaves manteca and drops you off in Stockton to switch to a bus that will get you to San Francisco, BUT, I found out that I could not buy a ticket in Stockton, due to whatever stupid regulations, there are regarding switching from a train to a bus or something.
better to get the train in Manteca and just make the transfer, no problem. I had to bribe the driver––just plopped a twenty in his lap and got on. Anyway, this might be too much info. hope someone can use it.