Can Accord and Satisfaction be bifurcated on an itemized invoice

This is going to be an Accord and Satisfaction question but let me give some background. I am a small residential concrete finishing business in Ohio. The customer requested a quote to put a concrete skirting/patio around their new in-ground pool after the customer had backfilled the existing excavated trench around the pool with gravel. The quote for the patio was $5,600. The customer then verbally asked for a price for the gravel backfill which we verbally agreed to a combined price of $6,500 for the concrete work and for 20 tons of gravel backfill with additional reasonable cost if it needed more than 20 tons. It required 28 tons of gravel so the final invoice was $7,300. It does not appear that there is a big issue with the final gross amount of $7,300. The customer was very hands-on with comments and demands throughout the project work. The critical item was that he filled the pool with water before we arrived and wanted us to put plastic (i.e. visqueen) over the entire pool and down between the future concrete edge and the side of the pool in order to prevent splatter from getting in the pool water. I told him that the plastic would prevent a good concrete finished edge up against the pool side and that he would need to cut the plastic away after the concrete dried which may leave some plastic showing. He said "do the best that you can" but insisted on his process. I told him that the normal practice is to do the work without water in the pool and have a solid edge between the poolside and the concrete in order to get a good finished edge. His dispute is with the quality of the finished edge but I am not asking for advice on resolving that issue. My question is with Accord and Satisfaction. My final invoice (invoice #1722 dated 10/4/22 for work that was completed on 9/23/22) for $7,300 is itemized as $5,600 for the concrete work and $1,700 for the backfill but it is all on one invoice (i.e. not separate invoices for the backfill and concrete work). I have had several discussions with the customer regarding the quality dispute and he refuses to let me on the property to assess and remediate. There is no dispute on the quality of the gravel backfill portion of the job. I finally offered a $500 goodwill credit to resolve the issue if he pays $6,800 which is did not accept. He verbally offered $5,900 as payment in full which I declined. He then sent me a letter in the general format of an invoice and labelled it "corrected invoice #1722". His corrected invoice is organized in two parts ($2,108 for the gravel and backfill and a $5,000 gross amount for the concrete). I have no idea how he came up with $5,000 as the gross amount for the concrete work when my invoice (and initial written estimate) shows $5,600. I also do not know how he comes up with $2,108 for the backfill when my invoice shows $1,700. In short, his gross amount of $5,000 + $2,108 = $7,108 as compared to my invoice of $7,300. I would have been fine with this difference but he then deducts $839.15 from the $5,000 to arrive at an amount of $4,160.85 for the concrete work. He issued two checks (one for $2,108 for the backfill and one for $4,160.85 for the concrete). The check memos say "concrete" on the $4,160.85 check and "backfill" on the $2,108 check. The checks do not say "paid in full" but his letter/corrected invoice, as well our discussion, leads me to reasonably assume that he intends the payments to be considered "payment in full". My understanding of Ohio Revised Code 1303.40 is that if I cash the checks, it will be considered payment in full under Accord and Satisfaction doctrine. My questions are 1) I assume that I should not cash the concrete check as it will likely be interpreted as payment in full. 2) Can I cash the backfill check which exceeds the backfill portion of the invoice and preserve my rights to collect the full amount on the concrete work? 3) If so, should I refund the overpayment of $408 on the backfill or just treat it as a deposit or partial payment on his account? 4) If I treat the $408 as a deposit, should notify him and, in that notification, should I state that I reject his concrete adjustments and request that he acknowledge that I am cashing the $4,160.85 check as partial payment of the concrete portion of the invoice. 5) If I proceed as stated in #3, and the customer accepts, can I cash the $4,160.85 check. 6) Do you have any other advice. Hopefully this has been entertaining to read and potentially be an example for your future blogs or customers. Please send response to denniswiser86@yahoo.com