First, let me welcome you to these forums Cliff, I hope you find what it is you’re looking for. I’ll try to help you understand a bit more about CM and profiling.
I’ll start with the bad news first, I guess. The profile is not something which is or can be neutral - only the device can be considered as such. The profile will attempt to correct for a device which is not neutral, but unless the profile is a B&W/greyscale/tinted greyscale, it can’t really be considered neutral. The problem here really has more to do with the printer and paper than anything else IMHO. As the 1400 is a consumer level printer, using dye based inks and just 1 black ink, it will always have a very difficult time trying to achieve perfect neutrality.
Consider that the black dye in the ink itself is more than likely not neutral at all, so even if printing with just the black ink, prints may still be non-neutral. This can easily be checked with your i1Pro spectro. Next, the curves you show in the screenshot are the condition the profile is trying to correct. There is only so much this printer is able to do as it was never created with the emphasis on being able to produce neutral B&W prints because a) it is aimed mainly at consumers and b) it is aimed at photographic printing, which for consumers, does not include B&W printing. The dyes/inkset were chosen to produce a pleasing, saturated, contrasty, punchy image with colours which ‘pop’ but none of that asks for or requires B&W neutrality.
You mentioned that you’re trying to create a better profile than the Epson canned profile. This is a very hard task as for starters, you are not using an Epson specified paper, so immediately neutrality, if possible at all, is far more difficult to achieve. In fact, the only way to better the Epson profile would be to use the exact same paper as the profile which you are trying to improve, otherwise your profile has nothing to do with an Epson profile. Remember too, most likely the Epson profile was created using high-end measuring equipment, likely costing several thousands of $$$ alone, the profiling application probably costs at least that amount, if not more, they likely would have averaged many prints, possibly from many printers to get a decent sampling of what will be out in the public’s hands and the creator of the Epson profile would undoubtedly be a very experienced colour management specialist consultant or engineer who has done this thousands of times before. So you’re asking a great deal of yourself to better that lot.
The fact that you mention both the Epson profile and your profile are not as neutral as you’d like indicates to me that the Epson profile is as neutral as this printer is going to get, so likely no amount of fiddling is going to help very much. You’d be much better off selecting a printer from anything in the Ultrachrome K3 range, of which there are a few in the same 19" size as the 1400. Something like the 2880 or 3000 or 3880 would produce neutral and beautiful B&W prints, without even trying, due to having a specific B&W print mode but even in their RGB print mode, will still produce much better neutrality than what you would be able to achieve using the 1400 and any amount of profiling. The 1400 was simply never intended to produce that sort of output.
Regarding ‘getting under the hood’, there is really not very much that can be done these days, or rather that should be done. I have been profiling my own printers and producing (fine art) photographic gallery quality prints for over 7 years now but never once have I actually tried to edit a profile for neutrality. I don’t even know if it is possible? What profile editing is mainly used for is matching specific ‘real life’ colours (such as a company logo, e.g. the red from Heinz Ketchup label). And even this is not for the faint-hearted as it is so much easier to ruin a profile than it is to improve it.
You asked if a larger target or better profiling application could possibly help your situation, but this indicates to me a bit of a misunderstanding of the basic profiling procedures or what a profile is trying to do. I strongly suggest reading a copy of either Bruce Fraser’s Real World Color Management or Andrew Rodney’s Color Management for Photographers to get a very decent introduction to just about everything that goes into profiling and how it all works behind the scenes. I have a spare copy of the latter if you’re interested, I could send it to you. PM me if you’d like me to do so.
Have you read through and understood the ColorThink Pro 3 user manual? I very highly suggest you do so and also perform all of the tutorials in both the ColorThink Pro 3 manual and also the ColorThink 2 manual as well. There are some excellent tips and hints in there and some great tutorials which will help you extend your understanding quite a bit.
I do hope I haven’t confused you (too) much. 
It really is a large can of worms you’re opening up. 
Essentially you need to slow down and as the cliche says, learn to walk before you run and also, put on a pair of quality walking shoes (ie an Ultrachrome K3 printer) and you’ll see how much easier things can be.
If there is anything you don’t understand in what I’ve mentioned just post your reply and (hopefully) we will eventually get you up and running.
