ADL is blind magazine with no floorplate. BDL has a floorplate. There have been many many different configurations of each. Some guys are confused and try to add different features to them which are irrelevent. If it has a floorplate it is a BDL. No floorplate it is an ADL. No other features matter.
Remington really confused things a few years ago when they dropped both the ADL and BDL. The CDL replaced the BDL with a trimmer more classic designed stock. The SPS was meant to replace the ADL as their budget gun.
All was good until they brought back the ADL and BDL in limited numbers. It makes things more confusing. The SPS and CDL are still just a version of a BDL. If you order a custom stock for any Remington you will order a BDL style stock if you want a floorplate, ADL if you want a blind magazine. It does not matter if the gun is BDL, CDL or SPS.
Right now the CDL and BDL are the top end guns. They just have very different stock designs. The CDL is more like the stock styles from the 20's-40's with classic lines. The BDL is a more modern stock style from the 50's-60's when everyone was putting tail fins on cars. The BDL is cataloged, but is only available in limited chamberings and is made in limited numbers. I have seen quite a few showing up in Walmarts lately, so it appears Walmart has made a big purchase.
The SPS is the budget gun with a floorplate. Basic matte finish, with a plastic stock. The ADL is basically the SPS with no floorplate and can be sold cheaper. The ADL is no longer cataloged, but is often seen at great prices in the big box stores.
Remington has in the past offered detachable mag versions. They are not exactly common, but I see a few at gunshows occasionally. If you can find one of these it will simplify you DBM requirement. If not I'd look for the cheapest used version in any configuration I can find since it will require major modification anyway.
I'd personally just go with an SPS or ADL and forget the DBM. That will add considerably to the cost and money would be better spent on a better barrel or optics in my opinion.