The length of your arms has nothing to do with the LOP of your gun. It has more to do with the way you stand, the width of your shoulders and the length of your neck. LOP requirements also change depending on how you mount the gun. If you have to lean your head over or if you can keep it straight up will all be factors in LOP.
I have a BT-99 with an adjustable butt plate that allows me to lower the pad. This lets me keep my head more erect. That gun has a LOP of 14 1/4" and is about perfect. I also have a Cynergy without the adjustable pad. If I mount it with the pad fully engaging my shoulder, I have to lean my head over more. That gun has a 14 1/2" LOP and is still too short. If I put an adjustable comb on it or an adjustable butt plate, the LOP won't have to be so long.
We cannot tell you what LOP you will need over the internet. There are just too many variables.
I can tell you this though, if you are comfortable with your Mossberg at 14 1/2", the Micro BPS will be WAY too short. I bought a BPS Micro Trap for my son. He is still too small for it, but I just had to get it out to the range. The 13 3/4" LOP is much too short for me, but I was able to shoot it OK. For regular Trap though, I would need a longer stock.
Do yourself a favor and take a little time to get educated on stock fit first. It will be worth the time and money. In fact it will save you money in the long run. The book "Stock Fitters Bible" by Rollin Oswald
will be some of the best money you can spend on shooting. He is a regular poster here and gives some of the best advice I've seen. Buy his book. It will save you money in the long run.