I have a JP Limited 1187 that I just finished modifying to a convertable Limited/Open shotgun, and having shot it in a couple of matches in Open, I think I found THE setup for me anyway. It came from JP with a 21 (22?) inch smooth slug barrel with rifle sights.
First I had my smithy put on the receiver mounted Da-Mar Scope Mount from Brownells (483-100-001) and put a JPoint on that. The JPoint on top of the Da-Mar is very low and doesn't change my cheek weld. I can also use the front sight on the barrel with the notch in the rear of the JPoint in case of dot failure, just aim about 4 inches low at 15 yards. I really like the dot sight closer to my eye on the receiver compared to mounted on the barrel like the JP Open Shotgun. Flip & Burn loading in Open is easy, and none of the sights are in the way. Converting to Limited is also easy; just remove the JPoint, the DA-Mar mount is not in the way at all.
Next I installed the obligitory Tec speed loader bracket and Arradondo "funnel". These are easily removable to convert between Open & Limited because they are mounted with extended trigger group pins.
Then I added the Briley compensator/choke setup from Brownells, (129-301-001 thru 129-301-008, take your pick) Also needed is the special choke wrench, 129-310-000. You may need to enlarge your gas ports, mine are now .120, test fire the final setup before drilling!
Lastly, add a 5 round extension tube for total of 10 in the tube for Open, or put on the 3 rounder for Limited, and I have a Limited/Open convertable shotgun!
With all the barrel mounted dot suggestions above, I just thought I would add my alternative of the receiver mounting, the setup works great for either Limited or Open, and I now have a great sight mounted for fall deer hunting!
JJ