Distributing entries to avoid the same team

[scross]

Hello,

Attached is a stripped down demo spreadsheet.
Normally there can be up to 140 teams and 8 categories.
Managers select names for events.

Ideally the first name selected from a team in each category is the fastest and they get placed in the centre lanes.
Have used random to distribute teams so that team A in the demo is not always in lane 6 of heat 1.
It also helps distribute teams across the heats.

However, at present I can end up with say 4 heats and 5 members of team A distributed across only 2 heats.
To avoid complaints I would like to move on from random and have a formula/mechanism to be able to check if an existing team member is already in the heat before inserting the next entry.

It could be that the distribution is triggered off a button click which would hopefully avoid endless background loops.
It could be that the distribution occurs on a change to the heat but this may result in a back ground lop.
Needs to run on Excel 2016 with 4 Gb's of RAM.
I started to look at if statements but quickly became over whelmed.

I would very much appreciate guidance of on how to achieve this distribution.
Thank you.