Learn English – Can you negate a positive without implying the opposite

The only more concise way to ask it that I can think of is

Was Tom in Professor X's class?

However, this changes what you're asking from confirming your belief that he was not to asking in a neutral fashion (that is, you have no a priori belief).

If you're wanting to keep it as a confirmation, something like your second option above is about as good as it gets:

Tom wasn't in Professor X's class, right?

I think part of the issue is the way you have parsed well off. Consider, for instance, that the Free Dictionary defines well-off as a hyphenated adjective, and speculates that it derives from "to come well off" where off in this case indicates "circumstanced" with the overall meaning then being to emerge from [sth] in good circumstances.

If we start with that phrase — to emerge from [sth] in good circumstances — and work backward, we'd have to emerge from [sth] in bad circumstances. From this, we can jump to bad off, but I think we should look more closely at the other phrase that was mentioned, namely "to come well off."

It's an odd phrase, but I found it in use in Google Books, so I tried the most obvious opposite "to come poorly off". Sure enough, that's in use, or at least it was in literary use in the 1800s. That suggests strongly to me that the most appropriate negation of 'well-off' is actually 'poorly-off'.

However, the phrase "to come badly off" is also in regular literary use in the 1800s, so 'badly-off' could be perfectly cromulent as well.

Suffice to say, depending on how you look at it, any of bad off, badly off or poorly off could suit.