What is the regulation regarding contact with IET soldiers following AIT graduation?

Hmmm....well you cannot find it in TR 350-6 because it does not exist. If you are a security hold, and your MOS requires the clearance, then you are not officially MOS qualified. This means you are still in student status which is probably the real reason you are still in the company. There should be no issue with you having contact with students in the course, since you are still that status. Now, you NCO's may not want you to have contact with them for a various number of reasons, but against regulation should not be one of them.

First, I would like thank SGM Carl Cunningham for his sincere patience in responding your borderline condescending tone. If you were an 18 year old kid, I probably would have just chuckled at your naivety while drinking my coffee. But you are a 24 year old man with a little life experience under your belt and therefore should have some sort of perspective of the "the bigger picture". There is no room for a sense of "self entitlement" in this organization. You are now part of a diverse team that makes up for less than 1% of our population. We are brothers and sisters working together in various capacities with a common goal and objective. Please refer to the "redundant" line two of the Soldier Creed as you "live to the standard the Army has helped you set for yourself". I will now provide you a lesson based on our creed as Non Commissioned Officers. Please refer to the third paragraph (of the NCO Creed) for my implementation of the following lesson/guidance/mentorship.
Think of Army regulations just like you would think of a Federal Law. They are guidelines put into place a a senior level that give us guidance in countless aspects of our day-to-day lives and operations but they do not necessarily apply to every situation. There are "grey areas" that don't necessarily pertain to current guidance. The Army delegates the authority to write further guidance to subordinate command levels to identify these "grey areas". You will often hear "you can add to, but you can't take away from" when speaking about Army regulations. If a specific situation isn't identified in the TRADOC regulation (ie. 350-6) it may be identified at your installation Brigade, Battalion, or Company level policy guidance or standard operating procedure.
AR 350-6 Chapter 3 Paragraph 3-2 B (4) gives your cadre the authority to assign you as the "adhoc Battle Buddy". As a DS I would much rather use a hold over for a battle buddy then have a Soldier miss training for no reason.
AR 350-6 Chapter 4 Paragraph 4-9 and Table 4-3 identifies security clearance requirements for your current MOS. If you read Chapter 4 Paragraph G Number (3) The 120th day from the PSI submission date, at which time the Soldier will either be reclassified into an MOS not requiring security clearance eligibility or processed for discharge.
The First Sergeants Barrack's Program (FSBP 2020) guidance from Installation Command (IMCOM)
"Permanent Party" barracks or Unaccompanied Personnel Housing (UPH) is utilized for traditional Permanent Party Soldiers. I can completely understand why your cadre want you housed with the IET Soldiers. It is one less thing to worry about. If your housed in UPH they are creating additional work for themselves for no reason. It is much easier for Command and Control (C2) purposes to have you housed with the rest of the trainees.
To identify a few of your other comments or inquiries below:
You are not "eligible for permanent party status" because you are not and will not be assigned to a specific paragraph and line number (position) in your organization. There has to be a specific position that you are slotted into. You would have to receive "official orders" cut, assigning you somewhere's within your current unit and then be assigned a sponsor and in-process into the installation. (alot of work) All of this is not going to happen for the simple reason that "you don't want to live in the barracks".
Congratulations on your promotion! AR 600-8-19 Enlisted Promotions and Reductions guidance states you are automatically promoted to PFC after completing 12 months Time In Service (TIS) and 4 months Time In Grade (TIG). "Everyone gets a ribbon for participation!!!!" Your lack of disciplinary actions should be commended? Thank you for not violating the VALUES that serve as our organization's foundation.
And last but not least you have "gained all that you can from being in IET status"? How about you help the other Soldiers in your organization who haven't "gained all they can". Assist them in areas of weakness. Take some of the burden off of your cadres shoulders.
In closing, you are a 24 year old man. Instead wasting time trying to find a regulation that gets you out of your "cumbersome and redundant" living conditions utilize this time to learn about your craft and basic Soldiering. Please do not be that Soldier that cadre has to give "special attention" to. The last thing you would want them to do is call your gaining FORSCOM unit and let them know they have a problem child on the way. I would be more concerned about gaining your security clearance than petty BS. No clearance means either discharge or reclass...........
What are your feelings about being in the Infantry?

You are in a IET unit. You are IET until you arrive at your first duty station, then you will truly be considered permanent party. Once you are permanent party soldier you are not supposed to converse with IET soldiers. Same goes for cadre. They cannot have contact for 6 months past the soldiers arrival to their first assignment.