First off... I own an esp ltd ex-350 and played through my mesa triple rectifier it sounds terrible. It's the pickups in the guitar. EMG HZ's are just not good pickups IMO. I have a couple of stratocasters, 1 with a seymor duncan hot rails and the other with a HB jr. and they both sound great. Also,
my gibson flying V sounds great through the mesa too. Clean, I'm sure the F-250 sounds really good. But distorted I bet it sounds a little bit dull. So, try this for settings:
for the switches in the back, you probably want the power on spongy, and the rectifier switch on tubes. on channel 3 (i'm assuming you have one of the newer 3-channel heads) turn the gain type switch to modern (you know that switch that says "raw, vintage, modern") and turn your gain all the way up. Now, turn the presence knob almost all the way up, maybe to about 4 oclock. Turn your bass to about 1 oclock, and the mid to around 8 oclock (almost all the way down) then, experiment with the high knob and get it up to where you want it. It should provide a decent 'screamo' sound. If it sounds a little too trebly, turn the mid knob up a little bit.
If you still can't get the sound you want after playing with the settings, consider this: The best sound I have ever gotten out of my triple rectifier, was with a $30 POS distortion pedal. In fact, it was
a danelectro black coffee. One of those crappy mini ones. Try a distortion pedal! I've noticed that sometimes with tube-type preamp gain it sounds a little gritty. Like the gain is not really 'tight'. It's hard to explain, but, I just like the sound of a solid-state gain with a tube power amp. I believe this is what you are looking for in your sound. I guess just try some things, and you should be able to come up with the sound you are looking for.
I just thought of this too: There are a couple of knobs in the back, and for some reason (don't ask me why) they effect your tone. They are for the effects loop and even with the effects loop off, or bypassed, or whatever, they still can have a factor in how your amp sounds. They are the effects send and return knobs. The small ones. I have those turned all the way up on my head. Try playing with these as well. The mesa rectifier amps are actually really difficult to get the sound you want out of them, but it's not because they are shitty, they are just different than most amps. Experiment with it. The more you play with it, the more farmiliar you will get with the sound. Play with the switches.. all of them are fair game EXCEPT the bias switch, which is in the back, and has two settings, EL34/6L6. DO NOT CHANGE THIS UNLESS YOU KNOW WHAT YOU ARE DOING. IT THE DIFFERENCE BETWEEN YOUR AMP WORKING OR NOT WORKING AND IF YOU CHANGE THE SETTING WITHOUT CHANGING THE TUBES TO THE OTHER TYPE, YOU WILL BURN YOUR AMP UP! But since you read the manual, I'm sure you know that already
Anyway, hope this helps!