Well its true that CEID does not issue PCCs for BV or tourist visa. However, you were under family visa before. Maybe try talking to Jamal in CEID Salwa or try talking to some captain.I am resident of Qatar and I am facing problem with Qatar police clearance certificate both for me and my husband. In my case I was under the sponsorship of my father from Sept 11th 2013 to March 1st 2018 and in order to be under husband sponsorship I exited and returned on 9th March 2018 under husband sponsorship. Now the problem is the CID issued police clearance certificate from 9th March 2018 to the date of my police clearance certificate application. So my doubt is will i get the police clearance certificate for the period under father sponsorship.
In my husband case he came to Qatar on Oct 2014 under business visa for 1 year without exiting. He received residence from 2015 to the date of police clearance certificate application. So kindly request to advise if someone has faced the similar problem.
If still not possible then yes definitely explain your situation in a letter of explanation.
As for your husband: no chance he can get pcc for BV. He definitely has to write LoE. Shouldnt be an issue.
I am sure by now IRCC would have noticed a pattern as this is not an isolated case.