> raise the ground (floating ground)
What ground? I don't see no ground.
The transformer winding is fully "floating". Think of a flashlight battery in outer space, except AC. No ground is present or needed. If you have a ground and want/need to connect it, you can connect it anywhere in the circuit. TO top, middle, or bottom of the cap-string, or even to the diode end of the transformer (though I don't see any use for that).
Practical items can matter. Common transformers can "float" up to about 500V across the insulation. The primary side is normally grounded at the utility company and fusebox. So if you want to multiply-up a high voltage winding to a very high voltage DC, you can get in trouble. If the winding is 200V, each cap charges to 280V. If you ground the bottom of the cap string, the center of the cap-string is 280V, the top is 560V, and the top terminal of the transformer will peak at 560V above ground. One end of the primary is at ground, the other end peaks at 170V or 330V, and maybe in opposite phase. So you could end up with 560V+330V= 890V across the paper insulation between windings.
That is why there is a second version with one end of the AC source (optionally) grounded. It is less efficient, but less abusive of the transformer insulation. If you need 20,000VDC, you will probably start with about 1,000VAC (which would probably have >2,000V insulation) and run about 20 stages of rectifiers and capacitors (on tall glazed porcelain insulators!). (Actually, for small current, you would pull the specially insulated 20KV transformer out of an oil-burner or neon-sign.)
> assuming that the wires coming off the transformer are not shorting together there
That won't work too well. While all schematics SHOULD have dots and bump-overs or equivalent notation to differentiate crossings from connections, sometimes you have to guess and pick the most likely (or less unlikely) interpretation.