Hi Carol, I am in the middle of supplementing right now and this is the advice I was given on the forum for fairly similar results to yours (not medically trained).
The most commonly recommended are Solgar and Jarrows, I believe on the basis they have less rubbish in the fillers! I buy mine off Amazon
B12 - buy methylcobalamin rather than cyanocobalamin as it absorbs better, I was also advised to choose sublingual tablets you suck to overcome any absorption issues (common). I am taking 5000 mcg daily and when tub runs out will switch to 1000 daily to maintain levels. It is water soluble so you will excrete any excess - aim for level of over 500 (GP prescribed cyano so bought my own)
You need a good B complex to balance the B12. (mine is prescribed)
Folate - buy methylfolate rather than folic acid, again it absorbs better - aim for around halfway in the range. mine is 1000mcg - if your B complex has this you dont need it separate.
Vit D - buy it as D3 soft gels as it is fat soluble so needs oil to be absorbed, take with the fattiest meal of the day - needs to be above 70 and preferally around 100. (i was prescribed a loading dose of 25000iu twice a week for 6 weeks then will switch to 1000iu daily as I work shifts so dont get any sun.
Vit D has following co factors which help to direct calcium to bones and teeth rather than to soft tissues
K2-MK7 100mcg seems to be standard strength - fat soluble
magnesium - choose magnesium citrate as better absorbed, mine is 400mcg.
Vit D is not excreted so you will need retesting after supplementing, especially loading doses as too high a level is harmful.
I take my Bs and folate together during the day and my D and co-factors in the evening with my heaviest meal, also magnesium makes some feel sleepy so evening is best. If you dont have much fat in your diet gave a couple of spoons of full fat yoghurt or a bit if cheese with them.
Take levo at least an hour before supplements or 4 hours after to avoid them affecting its absorption. If B complex has biotin stop it a few days before tyroid tests as it can skew results.
My GP accepted my Medichecks vit results so worth a try, tell him you have taken advice on here (the NHS choices recommended forum) and that getting vits right is essential to proper levo conversion. I am much less fatigued and foggy 5 weeks into proper supplementing.
Hopefully your poor vits are responsible for your poor conversion and RT3 levels at which point a levo drop might be in order. I refused to drop (test results on bio) until we got vits in order and can review properly. If he starts muttering about osteoporosis and cardiac issues - these are consequences of being hyper (unless you have other relevant history) which your FT3 says you are not.
Try this link:
The full research conducted by Flynn and Leese found exactly the same to be true for cardiac results but I have lost my link to the full article☹️.
The TUK diagnosis and treatment leaflet also has useful excerps, about 3/4 of way through (ish)
It might be worth getting your ducks in a row before changing to T3, you may find that its sorts conversion so that levo works for you, this would save the hassle (and cost) of sourcing T3. Also if you do both at once you don't know if you are feeling better due to improved vits or the T3 and T3 doesnt suit everyone.