to be honest when you are on T3 only therapy bloods are USELESS and should not be looked at.
'however' NHS doctors cannot 'survive' without looking at bloods, so:
do not take any T3 for at least 12 hours prior to your blood test (I leave 24 hours)
TSH will be suppressed on T3 only, especially on any dose of 40mcg or above
fT4 should not be tested as it will come back very very very low next to zero, however doctors do test it, maybe they want to see if you are 'cheating' and taking any T4 meds on the sly?
fT3 even though if it is above range it will still be ok, NHS doctors will not like to see it above range hence why you do not take T3 before a blood draw
I take 160mcg daily of T3 prescribed by an NHS endo, so NO it is NOT true that 60 is the maximum you should take, that is just a 'suggested' dosage on the BNF and some medication leaflets, the dosage should be INDIVIDUAL, so whatever dosage makes you well with no hyper-stimulation (hyperstimulation in signs/symptoms not in bloods!)