What are my options to do an unaccompanied CONUS PCS so that my wife can stay at my current assignment to finish school?

Unless your orders specify that you are PCSing to a dependent restricted location, you won’t have an “Unaccompanied Tour” (meaning you won’t have any additional entitlements that would come with one).

One clarification though. Since you mentioned recruiting duty, when you said "report to Knox early next year" were you referring to attending the Army Recruiting Course (ARC) and "I will be expected to report elsewhere probably in July" is referring to your follow-on assignment after completing school?

If so, then you will be sent TDY and return to the ARC and PCS from Fort Liberty after completion. Additionally, the "180 day limit" I mentioned below shouldn't be a concern as your PCS wouldn't happen until the summer of next year. However, keep in mind that the ARC is less than two months long, so you might be PCSing sooner than July (this all assumes you are going to the ARC of course).

So, the good news for you is the situation you are describing falls under “Housing Flexibility Options” (also referred to as “Flexible Housing Arrangements”) as one of the categories is “a spouse who is currently employed or enrolled in a degree, certificate or license-granting program”. You may request a flexible housing options starting up to 180 day before the PCS date and ending 180 days after your PCS date and one of them is “continuation of stay in government-owned or -leased family housing if they are living in such housing at the start of the covered PCS period.”

You’ll have to obtain approval from your installation* and it’s not guaranteed because it requires that remaining there would not impact the housing arrangements of other service members assigned to the installation. If you're staying in Public Private Venture (PPV) housing (i.e., privatized housing) then this option won’t be available. It's unclear from the website if Fort Liberty has converted all of it's housing or if it has a mixture.

Refer to the Military OneSource website* for in-depth details, but since it ends 180 days after your PCS date, it might not cover her all the way to December 2025 if you are PCSing early next year (if you're heading to Knox for the ARC, then it might not be an issue as you will be TDY and return .. depends on when you actual PCS date is). If you're not attending the ARC first, if you are able to get your date pushed back until mid-/late-June, then the 180 days should cover your wife through graduation.

Fort Liberty’s Military Support Office (MSO) should be able to help you out with more details and options.
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* Military OneSource Flexible Housing Arrangements - https://www.militaryonesource.mil/moving-pcs/plan-to-move/housing-flexibility-options-for-service-members-and-families-during-pcs-moves/

I would look at your orders carefully. If you're going the recruiting route then the recruiting school itself is a TDY so that should be on whoever you're attached to right now.

As far as the PCS itself is concerned: online I'm able to select whether or not I'm doing the travel with dependents. I think that means that financially your family is on their own until the end of 2025. If your wife's perfectly ok with that then there's that.

The other thing that you can do, well, more so your wife: is check her school's accreditation against wherever you're going to be stationed as a recruiter. Assuming the school is one referred to by the base's education center then in theory said school should be versed in students needing to transfer before they fulfill requirements. Of course, "should be" doesn't mean they are.

I'd bring up any and all concerns with your chain of command as they're valid concerns.