I have dealt with hypothyroid problems for a number of years although my dose is very stable and, by supplementing properly, I've gotten rid of all the side effects (hair loss, lethargy, etc.). The 4 hour wait is for iron, calcium and zinc but not the B vitamins. However, it makes no sense to take individual vitamins (such as the B12, or even the entire B family). The fact that a multivitamin makes you sick does not surprise me - they are very hard for a lot of people, and you're only absorbing 15-30% of it anyway. The rest is wasted and/or wreaking havoc on your digestive system. If your problem is in the stomach, you're probably reacting to the coating (shellac, wax, all kinds of garbage in there) and maybe to the fillers. If your problem is lower in the intestine, it's probably due to the fact that the darn thing just isn't dissolved. And if it's not dissolved, it's not absorbed. So you're still tired.
The AMA recommended that everyone supplement in 2002 so you're on the right track, but the Physicians' Desk Reference says that pills aren't absorbed well (that's where that 15-30% figure comes from). If you want the info, I can send it to you. It's an attachment so you'll have to PM me with your email address.
Anyway, the AMA says liquid is far better, and food scientists will tell you that premixed liquids don't have much shelf life. So powder you mix in liquid is the best, AND it has to have ALL the nutrients, not just selected vitamins. If you look at all the vitamin products out there, you'll see that most companies make a zillion different combinations to appeal to a huge market, rather than really making a comprehensive product. So we wind up with "complete" multivitamins and then they say "plus calcium" or "plus iron" or whatever. Makes no sense. The vitamin industry is not well regulated, so they can put pretty much anything in there.
Also, if the product is outsourced to another country for manufacture (even if a US company distributes it), you have no idea what you're getting.
I've switched, and for 5 years I have never been sick, and I work out at the gym 6 days a week with more energy than women many years younger. So it works if you do it right - and it's easiest with a company that provides free support and helps you connect with other people who have your same issues.
And I have a friend who was exhausted too - her doctor told her it was because she had 5 kids. Yes, but now she has 4 more productive hours in her day and is not sucking down that coffee or those fistfuls of vitamins. She's happier and isn't wasting money on a whole bunch of bottles of pills, but she's supplementing effectively with an absorption rate upwards of 90-95%.
Let me know if you want more info. You probably have more going on that just the thyroid issue, so it might make sense to reduce the prescription but do other things to help the exhaustion.