Masters in USA for my non-credited Bachelor degree

[mnish]

Ouch, I have a vibe that isn't going to jive with you...seriously.
From reading what you've entered, I am thinking you're out of luck.
The institution webpage hasn't been updated since 2014, their programs are all diploma level.

I'm not sure, but your chances are very very slim, if any, in transferring to a legitimate school.
If my calculation is correct, there's only 3 years from that school - total 90 credits at max.
You're missing a year of education that is "similar" to a USA degree. That won't equal a degree.

Here are my recommendations: some options to think about...
Your best option is to get into a bridging/degree completion program for a Bachelors Degree.
Then move on up to the desired Masters degree program at various institutions of choice.

1 - Find out which 5 schools in the UK that will accept your credits and go with them.
If they are a "major" university as you say, they should have distance/online degrees.
Go with them as those degrees are considered "same as USA Regional Accreditation".
Further to that, you can finish with them and take an online DBA in the USA! or another Masters!

2 - You mentioned there are 20 or so who have gone into a UK/USA degree, who are they?
Which schools are those? Get your applications sent to those instead of the ones you tried.
If they reject your application, you can try several Nationally Accredited degree providers from DEAC.
Again, I don't think they will accept 90 credits for a 120 credit degree equivalency, you may need
bridging courses.

3 - Evalution agency, did they say your "degree" was equivalent to a USA Bachelors? Having
it noted as coming from an unaccredited school won't really matter, as long as it mentions equivalency.
If it is, you can apply to the Big 3 and the Competency Degree Providers. Most of these are "subject
course evaluations", meaning it's a lengthy list of courses you've taken and equivalency to what's offered.

4 - Finally, I think you may be able to complete a year of extra studies to make up the bridging.
Meaning, you may have 90 credits transfer and take the remaining 30 credits to get a Bachelors in USA.
Then you can apply to a Masters program as most require a 4 year undergrad degree in equivalency.
Hmm, you may start quickly and do a BSBA/BA CS in less than a year!

Furthermore, from reading what you typed, I feel you're phishing for info to place your "non"
accredited courses into an accredited institution, you maybe lucky, but it's going to be very rare.
Again, most institutions need the evaluation and also do this case by case basis, you need a lot of luck.
Apply away, it's your only option. But the bridging program is the best/closest to what you need.

I graduated in 2013 and completed 2 years work experience. And they awared me a bSc in software Engineering.
I have a 142 credits in my transcript