TuneECU lets you read the current map and save it to your laptop. For the cable, look for something that supports VW/Audi cars since that will support the specific ISO standard Triumph uses (ISO-9141-2). This should work: https://smile.amazon.com/dp/B00K6498D0
(rubs hands together)... Niiiiccccce! It doable then. If happen to have a Windows laptop. You can buy a VAGCOM cable ($20 on Amazon) and Nissan Data Scan II. It will allow to reset the fuel trims, idle air relearn AND set the idle rpm plus tons of other things. The 03-05 are the easiest to deal with (software wise) but in 06+. The BCM ID's were changed so a few things can't be done with that software. I can't recommend it enough though. I have an 04 and 06. Works wonders helping dial things in.
Nissan Data Scan 2: https://conceptzperformance.com/datascan-2-consult-ii-computer-interface-system-diagnostic-software-vq35de-nissan-350z-infiniti-g35-fx35-s1449-ds2_p_28300.php
Sure, it's just a VAG-COM K-line cable like this: https://www.amazon.com/VIMVIP-VAG-COM-Scanner-Compatible-Volkswagen/dp/B00K6498D0
The actual software used for reading/writing to the ECU is called nisprog, and Romraider is used to modify the ROM binary. It only works for -06 and older 350z and other nissan ecus that accept flash commands via the K-line. So unfortunately HR engines can't be tuned with it yet.
There's a short tutorial on how to flash the ECU here: https://www.romraider.com/forum/viewtopic.php?f=64&t=14867
I had an issue with my airbag light being on, but I was able to clear it with one of these cables, and VCDS Lite which is free, but still has the capability of clearing the airbag light. I'd say it's worth the few bucks trying that before dishing more into it. Also $1200 seems like a lot, so I'd look into German specialty shops and see if they can do anything.