Is there a "correct" implementation of persistent/stick connections for balancing RDP?

Question

linux

At first glance, the task is quite simple: in the absence of a connection broker, it is required to organize balancing of RDP connections to several terminal servers.
It would seem that ipvs, haproxy and others provide a ready-made solution, but the problem is that the implementation of persistent / stick connections in these tools is such that the entry from the persistent / stick table is deleted after the specified timeout expires, regardless of whether the connection is currently active, corresponding to this entry. After deleting an entry from the table, breaking the connection and reconnecting will lead the client to an arbitrary backend, and not to the one where his session was left. I want to minimize the likelihood of this happening. You can increase the timeout to several days, but this option, in fact, kills balancing, so it is not considered yet.
The problem can be solved by changing the record management algorithm in the table: delete the record after the timeout expires, but the countdown starts not from the beginning of the connection, but from its completion. The value of this timeout can be coordinated with the lifetime of an inactive session on terminal servers, and thus obtain a solution that guarantees a consistent state of the system.
Actually, this is the question: are there balancing tools with the described implementation of persistent / stick connections, when the countdown to deleting an entry from the persistent / stick table is activated not at the beginning of the connection, but at its completion?