To my mind, Dover/A20 TAP is a tool, the
implementation of which is aimed at addressing traffic congestion and air quality in the town - see
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/486735/A20_Dover_TAP_English.pdf&sa=U&ved=2ahUKEwjfnIvv96juAhVMSsAKHZKfCGsQFjABegQIBxAB&usg=AOvVaw09QnXaRFSqP-MpP5qDPt-b. (Note that this guide - to mk1 TAP, was issued by Highways England.)
The DfT(?) reply starting "Thank you for your email of the 18th of December 2020 regarding the activation of TAP 20" is, I think, a distraction; the issue is who designed the tool, why in that form and under what power, because that is who would have to amend it.
I can't actually find the Traffic Regulation Orders that I assume created the A20 and A256 TAPs, but judging from
https://www.legislation.gov.uk/uksi/2014/3415/contents/made, I'd guess the (then?) Highways Agency, approved by the Secretary of State for Transport (the DfT). So a straightforward question for the MP is: what is the legal basis for TAP20?
Note that the TRO for TAP mk1, which was broadly welcomed by politicians at the time - see
moderngov.dover.gov.uk/documents/s16462/Minutes, was found to be faulty and was replaced.
https://www.dailymail.co.uk/news/article-3690003/Vigilante-grandmother-paves-way-hundreds-motorists-overturn-speeding-tickets-convincing-court-Highways-Agency-s-paperwork-order.html refers. The fault is interesting and one wonders about the replacement Order.
TAP was also the subject of an FOI request:
https://www.gov.uk/government/publications/a20-dover-tap-foi. Note the temporary/draft sense of the tool as described by... Highways England.
Finally, although TROs are quite capable of pinpointing, say, a specific layby, I suggest that the reason why the head of the A20 TAP was placed at the Military Hill roundabout is so that LGV queue-jumpers could be turned back - see the Highways England guide above. I suspect that's a point you need to consider, although the underpass further back could potentially, I guess, be modified for use by policing vehicles to access a relocated queue head.