First to answer your question on the scope. Most of my Handies wear mid price range 3-9x40s or 50s on medium to high rings. My old eyes like the larger objective lens. Recently, however, I was looking for an inexpensive 4x32 to play with on my 32-20. I found the most inexpensive scope on ebay...an Aim 4x32 with rings and free shipping for 37.95. I bought it as a joke on myself, thinking to put it on my 7 year old grandson's .22. I was amazed. It is sharp and clear and takes adjustment well. I bought another and put it on my .45LC carbine. Now, lets see if it handles recoil. 100 rounds later it is still going strong. Below is the 50 yard sighting in target with the .45LC and the Aim scope. The last 3 shots center are one hole.
Now for the accuracy. My Handi Maxi likes stouter loads...158 gr. .38s at 1000, 158 gr. Mags at 1700 and 180 gr. Maxies at 2 grand. If you speed them up, I think they'll tighten up.
Good luck,
Pete