Question concerning letters of employment

Hi there I hope everyone is doing well today. My partner and I (I am the sponsor, my partner is a Indian citizen) are applying for a spousal visa. We are currently within the UK and have been cohabiting for more than 3 years. We are also married. As neither of our salaries meet the £29,000 salary mark (mine £27,840, her's £26,665) we are both having to provide evidence of our past 12 months of employment. I've worked at 4 places in the past 12 months, and my partner has worked at 3 places. We have both worked almost 7 months at our existing jobs - typical office work - and this is where our salary is from, however we both were working more customer service facing roles only 9 months ago or so. The problem I have found is that while all the other employers I have had over the past 12 months have provided the letter of employment laid out in the application, one of the people I worked for is delaying their time getting back to me. Unfortunately this person isn't very pleasant and though I hope not, I could see her outright refusing to give me the letter of employment.

I have my payslips from the employment, and a P45, however I stupidly threw the contract of employment away as I didn't think we would need it given the 6 months of proof I thought we had to give.

My partners current post studies work visa runs out on the 25th of september 2026, and my last paycheck from this person was the 30th of June last year. Given the shorter time horizon in people's experiences, would it be better to delay our submission to the first day of july, or would it be better to submit our application as soon as possible and if this previous employer hasn't complied just state that in our cover letter attaching my payslips and p45 from her?

Also, do each of the letters of employment need to be signed by the employer as well? I will have three of the letters of employment signed by the end of today, but I was wondering if it is mandatory or not.

Thank you so much for any and all of your help. And I hope that you are having a great day!