Not knowing what your cartridge's specified VTA is, or what VTAs you might actually be running with the three mats in question, I'm going to punt on the angle issue. I will venture to say, however, that unless the stylus is a fairly radical line-contact, spade-shaped configuration, I'd guess that the mat differences are responsible for most of the audible changes, as long as the set-up got the VTA essentially correct to begin with.
It's not surprising that you would hear the largest degree of improvement from using the clamp with the least good-sounding of the mats; that is the one that will need help the most. The better mats will get you more of the way there without the aid of a clamp, while still benefitting from its use.
I'm not familiar with your particular model of clamp, but if it's typical, with a diameter that's just a little smaller than the record's label, and a clamping surface profile that is lowest around the perimeter and higher towards the center spindle, then you may need to shim up the mat surface center about the spindle, with a compressible washer placed over the spindle, under the record. Effectively raising the central mat surface slightly above the level that's underneath the record's grooved portion, creates a small downward dishing of the record when the clamp is applied, which ensures near-complete contact of the record with the mat in the area between the lead-in and lead-out grooves. The washer should not be larger than about 3/4" in diameter and about 1/8" thick, and is commonly made of felt, although sorbothane or cork can work too.
However, if the mat surface is not entirely flat, but rather is contoured to be depressed in the area under the record label, then you may have to add another, non-compressible washer, made of plastic, hard rubber, cardboard, or metal, below the soft one, with the right thickness to just compensate for the mat's center depression and bring the bottom surface of the upper compressible washer to the same height as the main mat surface. You'll have to push down on the clamp before tightening in order to get the desired downward dish of the record, but be careful about trying this with certain older vintage records made from styrene or shellac, which will not flex like modern vinyl, and can break. Taking these measures should prevent the clamp from pushing the record's label into the soft mat and raising up around the edge, thereby achieving proper coupling of the record to the mat and platter.
It's not surprising that you would hear the largest degree of improvement from using the clamp with the least good-sounding of the mats; that is the one that will need help the most. The better mats will get you more of the way there without the aid of a clamp, while still benefitting from its use.
I'm not familiar with your particular model of clamp, but if it's typical, with a diameter that's just a little smaller than the record's label, and a clamping surface profile that is lowest around the perimeter and higher towards the center spindle, then you may need to shim up the mat surface center about the spindle, with a compressible washer placed over the spindle, under the record. Effectively raising the central mat surface slightly above the level that's underneath the record's grooved portion, creates a small downward dishing of the record when the clamp is applied, which ensures near-complete contact of the record with the mat in the area between the lead-in and lead-out grooves. The washer should not be larger than about 3/4" in diameter and about 1/8" thick, and is commonly made of felt, although sorbothane or cork can work too.
However, if the mat surface is not entirely flat, but rather is contoured to be depressed in the area under the record label, then you may have to add another, non-compressible washer, made of plastic, hard rubber, cardboard, or metal, below the soft one, with the right thickness to just compensate for the mat's center depression and bring the bottom surface of the upper compressible washer to the same height as the main mat surface. You'll have to push down on the clamp before tightening in order to get the desired downward dish of the record, but be careful about trying this with certain older vintage records made from styrene or shellac, which will not flex like modern vinyl, and can break. Taking these measures should prevent the clamp from pushing the record's label into the soft mat and raising up around the edge, thereby achieving proper coupling of the record to the mat and platter.