I thought I should update on my progress fixing this issue, and a general catch up.
I took the car back to Veloces to have another go, which I was disappointed to have to do after researching and spending so much already....
After a bit discussion we decided to replace the EGR unit. A blanking plate was discussed, but as this seems to give dash warning lights I decided against. A remap was also mentioned, as it can ignore the EGR, but as the EGR was likely faulty, this would still be a problem.
Veloces had also forgotten to replace the under engine valance, but not a major problem. Irritatingly the cruise control had also stopped working in the mean time, and they spotted nails in both rear tyres - oddly. So in for another £300 odd...
The car took them a day, so pretty good, and on the drive back from picking it up I was nervous for the hesitation issue to reappear, but I'm glad to say it didn't, so it seems we got there in the end.
It seemed odd to me that this Owner Group did not have a definitive answer to the stuttering problem, when it is clearly stated as a known fault on FIAT user groups. I found a pretty succinct FIAT recognized fault notice on this hesitation/stuttering at 2000rpm problem, and I attach it here in the hope it helps others.
I'm off for a long drive tomorrow, and hopefully back in love with my 147.
And now I'm thinking of that remap, and perhaps something to improve the slightly jiggly handling. An anti-roll bar??
I think veloces could take some responsibility for telling you removing the EGR brings up fault codes..well it does unless you have the EGR mapped out, if they suggested the re-map they should have told you this would solve it IF the remap they provide has it mapped out if not then why?... Autolusso's EGR delete with 180 map is great, it was around £150 and I ran it for a year and 30k with no issues before upgrading to my hybrid set up. highly recommended reliable and enjoyable map.
Also the fault you describe is very generic diesel power train related stuff and can be anything from sticky VNT , to failing MAF or MAP sensors a small tear in the vac lines, dodgy solenoid switch, boost leak, or even a failing lambda sensor which often presents like MAF failure.
its hard to correctly diagnose over the web without codes, but again to be fair it was suggested in two of the answers you got.
re the handling, well eibach ARB's are a really good upgrade and sort the body roll enormously but in addition I would look at shocks and springs as well..the whole eibach kit is a good idea, I have it on my GT, transformed the handling from soft and wallowy to tight precise and reactive, steering feel is much improved as are the overall handling characteristics of the car...it also looks a whole lot better lowered.
Quaife Diff is also a worthy mod and if you are re-mapping you may as well get rid of the EGR once and for all. it will only cause issues in the long run.
with both the GT and the 147 1.9 JTDm its up to you how far you go, anything from a modest re-map to my eventual 240 BHP example is achievable.
it's entirely up to you..