After looking at maps on the NLS website, my interpretation is that the LCDR rail level from its Blackfriars Bridge into Holborn Viaduct is about 50 feet (above sea level), with Queen Victoria Street and foot of Ludgate Hill (where the railway crossed) being 25 to 30 feet. By Farringdon station, roads are 45-50 feet, with the Met Railway being about 22 feet (estimate).
Assuming that the north end of your through station connects to the Met (somehow), that defines the levels (and change thereof) needed...
But - simplifying - the station proposed seems to be an equivalent - in place and height - to City Thameslink: from which, southbound it is about 1 in 30 up to Blackfrairs and the bridge. For steam, straight off the platform end, that is very steep (how does it compare to Camden Bank or the climb out of Glasgow Queen Street?) - undesirable if not impossible. So probably a lot of modeller's licence required to fit it all in.
Probably misunderstanding heights, as whether they are feet or metres. Regarding the Snow Hill incline, it was a combination of short trains and bankers to get it to work...
But there were Victorian proposals for the sort of station being suggested - a through 'city centre' main line station in the Fleet Valley - given that (AIUI) these were at least prepared to put to Parliament, these must have come up with a solution to the levels issue. Whether there are any details available anywhere, I've no idea.