ILR application - Change CoS in 6th year

Hi,

Hope you are good. My name is Mona and I am on a Tier 2 visa with an employer and this is my 6th year on it.

2010 I came to the UK in Oct - Tier 4
2011 Got a Tier 1 PSW - Got a job as an Artist 3411 with my current employer.
2013 Employer applied Tier 2 - exempt from the Resident Labour Market Test. Not on the shortage list.
2016 Visa renewed on a different SoC i.e. Graphic Designer 3421. No Resident Labour Market Test again. Not on the shortage list. My salary is £27000/- my employer is also spending around 7k on a training course for me. The extension expires this Oct.
2019 Now I'm in my 9th year here in the UK, because of the 35k salary catch I cant apply for ILR.

I am doing a lot more Web Design and Development and that's what the training is in. Could I request my employer to change my CoS to 2137 Web Design and Development and is there a way to show my training cost in my salary that I can talk to my employer about?

I am looking for any suggestions based around what my next steps should be.

A Tier 4 visa to study Data Science (which I have been wanting to do for a while but will be tough financially). Basically, eat up all my savings.

A partner visa? I'm living with my British Partner (Self-employed) and it will have been 2 years in Oct this year. Before moving in together we were living in a house share together (not our own place).

Any help would be welcome as this is basically all I'm thinking about atm.

Thanks.

Any help would be really appreciated.