Looking for advice regarding physical boards and non-numeric effort values

At my suggestion, the team has agreed to possibly switch from numerical points values to something more abstract, specifically t-shirt sizes, as we've been finding that using numbers has led to a bit too much of a mindset of using them as literal units of something rather than abstractions, causing a mentality of treating points values as a score and trying to convert points into time values. Also, introducing a physical board in addition to our Jira board

The former of these I suggested as a possible alternative to points purely because I've heard of some dev teams having some success with it, the latter I've had a bit of experience using and did find that it helped team cohesion and company visibility, but am not exactly seasoned in its use. If anyone who's been in teams that used either of these methods has any insights into problems they may cause and ways to deal with them I'd appreciate some advice. Currently I understand the general gist of their value, but may struggle to answer more specific questions on the minutiae, particularly from management, who are more results focused than process focused