That was Marco's point, not mine. My point was that grounding one end of the secondary makes the other end a severe electrocution hazard, with no GFCI protection, even if there is GFCI protection on the upstream supply. Presumably there is some conductive liquid in the O.P's centrifuge tube, contributing to the hazard if any leaks or spills.
Also, be careful *what* you ground and and *where* you make the ground connection - get that wrong, and you are one broken wire / bad connection from making the exposed metalwork an electrocution hazard, 'live' with the HV AC.
Note the number of deaths that have occurred in the USA due to mishaps with home-built
'fractal woodburning' equipment, which is commonly based on a repurposed microwave oven transformer. Like the O.P's proposed setup, that has one end of a HV secondary grounded, + presence of conductive liquids.
IMHO, interlocks and guards to block access to the cap with power on, and to prevent power being applied with the cap removed are essential.