Went to a Titleist Thursday iron fitting - Results and feedback.
if you take a more unusual maybes overall viewpoint of the possible issue from the opposite end of the spectrum of the by starting to look at results from the elite player & pga tour pro then that will trow up some interesting comparisons
you'd get an approx average with an 8i of swing speed 87 mph ball speed 115 mph carry distance 160 yards
average swing speed increase through the irons is about +2mph - so 7i @ 89/90mph ball speed 120 mph & the approx gap in carry distance goes up(or down) by around 12 yards each club so average 7i carry distance is 172 yards
average AoA for 7i is around -4.3 & average spin rate is around 7000 - 7100 rpm & average 7i SF around 1.33/1.34 - & the 7i loft maybes around 34º on average
with a game improvement design iron so designed with lower static loft for lower spin rate but maintaining launch angle a 7i here would be generating off of a good strike a much lower spin rate maybes average would be more around 5000 rpm
so can kinda extrapolate some & draw some observations over the numbers you experienced
one # that kinda stands out is ball speed which at 107 mph with 86 mph swing speed that number is a tad low so efficiency of strike isn't quite where it needs to be
that says there's something goin on at strike - so although maybes the experience of the strike is a reasonable good one - the quality of the strike is a bunch off
so it's just where on the club face angle most likely definitely with regard to where on the vertical axis of the face (& also to a certain extent where on the horizontal axis) that strike location is
along with that probably the relationship of face angle to path control of not just the feel of where the club head is but where the face is & what angle on primary the vertical axis is being presented at strike - tell tale number here being the dynamic loft being presented - so optimum strike 'compression' of the ball is a tad off
say strike is good at lessons but is that from LM data? so from SF #'s & AoA plus dynamic loft & ball speed LA & face to path #'s - or is the strike just being assessed visually through ball flight alone ?
would get a roll of impact tape - or a can of foot or dry shampoo spray to coat the face - to start really looking where strike is paying particular attention to around what groove on the face angle the middle of the ball is being impacted at - plus how far left/right of horizontal center it is - if strike is a bunch higher on the face then you've got to start looking at the angle of delivery of the shaft into impact as well as the other numbers
in general shafts are for fine tuning they change stuff but fairly small range of amounts in terms of spin rate - folks who deliver fairly consistent impact conditions even if those are not quite optimum won't find the range of numbers to be mega substantial - say if those impact conditions numbers give a fairly constant -AoA # with an iron & a fairly constant dynamic loft number with a strike a tad higher on the face angle than would be optimum they will still get very similar outcomes in terms of spin rate & ball speed & carry distance
in essence the issue is really about club face angle delivery conditions & strike quality - & what you've been asked to work on through lessons should give some clues as to what the issues in the swing motion are to be able to improve
often times see issues like this which is about at the sharp end where in the swing arc 'release' is starting to happen often times it's occurring too near the trail thigh
so although the 'experience' of strike in lessons & on the range is a pretty good one it's not yet quite where it really needs to be