I'm not sure if this helps as slightly different application to yours but our FLR (M) application in 2017 had a similar requirement as what you're saying and gave more detail as to what was required. Our ILR (M) checklist in 2020 only had one sentence (6 letters addressed to us for the past 2.5 years) so I just used the guidance from our previous application which was as follows:
Items of correspondence addressed to Mrs choc_mouse and Mr choc_mouse at the same address as evidence you have been living together since your last grant of leave in this category, or from the date you first started living together, up to a maximum of 2 years.
Items of correspondence should be addressed to you jointly or in both your names. The dates of the items of correspondence should be spread evenly over the whole 2 years. They should be from at least 3 different sources. If you do not have enough items in your joint names, you may also provide items addressed to each of you individually if they show the same address for both of you. For example - 4 items of correspondence in joint names to the same address and 2 items addressed to each partner at the address. In total 8 items would need to be submitted. If you and your partner have no bills or correspondence in joint names to the same address and 2 items addressed to each partner at the address. In total 8 items would need to be submitted. If you and your partner have no bills or correspondence in joint names, you will need to submit 12 items (6 each) of correspondence evidencing that you reside together at the same address. Documents provided must be originals.
Examples of acceptable items include:
• Letters or other documents from government departments or agencies, for example HM Revenueand Customs, Department for Work and Pensions, DVLA, TV Licensing
• Letters or other documents from your GP, a hospital or other local health service about medicaltreatments, appointments, home visits or other medical matters
• Bank statements or letters
• Building society savings books or letters
• UK Visas & Immigration
• Council tax bills or statements
• Electricity or gas bills or statements
• Water rates bills or statements
• Mortgage statements or agreement
• Tenancy agreement(s)
• Telephone bills or statements
So I thought you could submit documents not in joint names as well if you're really struggling, but you just have to submit more documents...someone will correct me if this doesn't apply anymore.
Regarding the evenly distributed bit, they want to see evidence that you've continually lived together. If all your documents in joint names are dated Jan 2018, it will likely be
insufficient, because they want to know you were still living together through 2018, through 2019 and now 2020. Usual guidance is to have some evidence every 4 months.