Learning the zone system isn't easy and you seem to have learnt quite a bit so far. I recon it's a good idea to go through the whole piece of quite tedious work at least once in order to grasp the whole concept.
Now, there are many variables where changing one will affect others. So it's very important that you don't change more than one at a time. At least until you've become familiar with how each one works.
Developers does have different characters, so changing developer will probably not give you an identical curve. As others above have pointed out, it seems like you should add a bit more contrast to your negatives, as they are a bit soft. Most developers does have a linear behaviour in between say 20-30 centigrades, so it's fairly safe to say that if you rise the temperature from 20 to 24 deg. you will have to cut the time by e.g. 25%. There are tables which can be found at e.g. Ilfords website which will sort this out.
Also, part of this linearity is that you can vary the developing time to affect where the zones fall. This linearity does vary with different films and developers (and concentrations of developers). With most common film/developer combos you can quite easily adjust the developing time to accomplish from N-2 to N+2. Part of the testing that you are doing is finding these developing times, where it seems like you are trying to find the correct time for N+-0 at the moment.
(There are some films which doesn't respond very well to e.g. N+2 or N-2. The same goes for some developers which may exhaust if you are trying to pull to much out of it. I would for example not use D76 1+3 if I wanted to do N+2.)
Anyhow, the times that Ilford suggests are starting times, intended for the beginner. These times should give "acceptable" results and they are very much "middle of the road". I.e. they will give contrasty negatives from full sunshine, but on a soft grade paper they will give a decent print. A harder paper is needed for the overcast sky shots... What you are doing now is to fine-tune this developing time so that you get a "perfect" negative which will print very nicely on grade 2 paper. But if I use a coldlight enlarger, I would need a grade 3 paper instead (or develop some 15% shorter time)...
Another question is "Why do you calibrate?". I cannot speculate in your reasons, but I know why I do some calibration work: I have my own working place, with my own equipment. If I develop by hand in e.g. a Paterson daylight drum, I have a certain agitation pattern. My thermometer may be off by say one degree. My water supply may be very alkaline or acid. ... In short, there are many variables which need to be spotted down. For myself, I have invested in a used Jobo CPA2, so that I get similar results in terms of agitation and temperature from one occation to another.
But this is only part of the whole deal. If Ansel Adams would have made his tests today, he would have found that using modern state of the art Schneider/Rodenstock glass would affect his results a great deal. With this I mean to say that part of what you are calibrating is your own equipment, ALL of it. While I do use Stoeffer step wedges, they are of limited value, as they don't show how my lenses, exposure meter, shutters etc. affect the film.
To make a long story short: The results of your tests shows that you need to add some contrast to your negatives. This is (hopefully) why you conducted the test in the first place. All of the advice above says what I'm about to say. It seems like you are some 10% short in developing time, so add another 30 seconds. It's as easy as that.
Then, do yourself a favour and stick with Ilfosol for some time, say some 200-300 rolls or more of actual photography. Once you come to terms with it and can figure out its pros and cons, this tedious calibration work will have paid off. If you are impatient and switch developers you are not really learning from the experiences you are having right now, but you are rather having the same problems over and over again.
By the way, personally I don't do the full zone system calibration anymore. It's too much work. But I do test the paper, so that I know what grade it really is at different filtrations. I also find out (more like ballparking really) what my developing times are for N-1½, N and N+1½. But if I come home from a trip, I develop one film and check if I'm pleased of if I need to compensate. Then the rest of the film is developed.
The +1½, 0 and -1½ comes from what I think Phil Davies calls this "the five finger method", which suits me and my Hasselblad with three backs very well.
//Björn