One way the Soviets could improve the consistency of the 91/30 accuracy was to wrap the barrel in felt around 7 inches from the end of the barrel, held in place by the upper band and the bands. It is essentially a nodal damping method. I forget but believe the felt was between 110 and 120 mm long. Apparently it was approved for use in both competitive and sniper rifles.
No idea on the average improvement, just read about it years ago and put down as a note.
The Soviets did make low end match rifles out of the 91/30 rifles, with the standard barrel. Some examples are shown in the book "Competitive shooting" A.A. Yur Yev. 1973.
They are shown on page 376 and include the AV, AVL, and BI 7.72, with the AV being nothing more than a regular 91/30 with a slightly shorten barrel, rear sight removed, restocked with a near military stock and an added target sight, set up for 300 m shooting. The sight adjustments were 1.5 cm at that distance on all of the 7.62 models, slightly better than the 2 cm which is standard with western European sight adjustments of that era (10 cm 10 ring @ 300 M).
As far as ammunition, "target" grade cartridges showing D100 of around 10~13 cm @ 300 M (20 shots). The extra cartridges were supposed to show under 9 cm 20 shot grouping at the same distance. The best "extra" lots will show grouping on the order of R 2.5 to 2.7 cm and D100 of 4.8 to 5.1 cm, which is right in line with the GP11 better production lots.
That said I have no idea about how well these rifles shot, as there is precious little information on them and the expected Extra accuracy combined with the various Mosin based match rifles or even the standard service rifle..