There's a good chance your carry handle sight is taller than the M&P 15-22 rear sight, but I don't have time to caliper them this morning.
Many commercial detachable handles are designed to shoot with the M16A2 front sight, not the slightly shorter M4 front sight. Getting better these days, but the commercial guns have been using M16A2/A3 spec front sights. Many M4 clones have M16A2 front sight towers.
The M16
A4, the flat top version, barrel is a different part number than the M16A2/A3 (both of which have fixed handles). The M16A4 and M4 use the same detachable handle. I recall the M16A3 was developed for the sea services to fit a special need. There aren't that many around.
As far as the US military is concerned, the front sight tower is a permanent part of the barrel along with the barrel extension. So there's no part number for the shorter (usually F-marked) front sight tower used on the M4, M4A1, and M16A4.
Please note there is no "A3" upper receiver as far as the M16 is concerned. The M16A3 has a SAFE-SEMI-AUTO selector and a fixed handle. The M16A4 is SAFE-SEMI-BURST with the detachable handle. Same handle as the M4/M4A1 and had the corresponding shorter front sight tower.
If your handle shoots excessively high you'll need to find the M4/M16A4 height rear sight assembly or a complete handle designed for these.
The markings of 8/3 and 6/3 are no clue to the commercial sights, they can do what they want.
Note the differences in the actual rear sights. M4/M16A4 on left, M16A2 (and A3!

) on the right.
-- Chuck