Usually the distances are not too challenging, maybe 7 or 15 yds at most? What is the CEP you are achieving at these distances? CEP is based on a 50% probability circle (or ellipse) about the bullseye center, not the MOA grouping around a floating mean.
One of the RSO's at KHSC told me that there is a bay on the left of the pistol range where you can set up a Ransom Rest to check out the inherent accuracy of your handgun at 25 - 50 yds. The RR has to be special ordered with a grip holder for your 1911. You'll need to contact the owner's wife in Arizona to order the device. Buying one of these means you are heading down a rabbit hole which will get deeper and deeper. Every week you'll be practicing until you bond with the new handgun, trying out new ammo, sights, grips, etc. You may even become a wind reader. 
At 15 yards with my VP9, I can hit avocado grouping at my POA/POI. This is for slow to moderate speed. So I expected the M45 to do the same or close, I would have been happy with grapefruit size grouping. My low shots were about small jabone grouping. But the POA/POI is what bothered me more. Had it been 5 inches higher and small jabone grouping, I would have accepted that more. At least my low shots are some what consistent.
At 5 yards and the VP9, I'm tangerine grouping with moderate speed. For the M45, I was low about 2-3 inches of POA but tangerine grouping.
So the POA/POI is my issue right now. More training is needed.
At 25 with the VP9, I can hit an index card with 2-3 of 5 shots. The shots off card are to the left of it like 1-3 inches. With a G19, 5 of 5 are on the index card. This is slow fire only.
I do not plan on buying a holder or like device.