Is there a way to implement overload work?

Is there a way to implement overload work into the program? My training partner and I noticed this past week when doing out test days that it was hard to get used to the heavy weight after using mostly Submax weight through the cycle. There was a feeling of instability and reduced confidence when attempting the maximal weights whereas before when we used a program with overall higher intensities, the weight felt stable and we had more confidence. For reference I am running the advanced medium load program on the app and he's running the advanced large load of the app. Maybe adding in singles or doubles at higher intensity after the main work sets so that you get a feel for the heavy weight?

I have recently added in heavy singles into my training. I'd work up to my first work set as per the app, then add on some weight and do a single, then complete the rest of my work sets. I.e. if you were prescribed 80% for 5x3 on the Squat, I'd do 1x3, 1x1 then 4x3. I do a heavy bench single every week, and alternate between squat and deadlift every week (i.e. squat single every 2 weeks and deadlift single every 2 weeks) - figured I didn't want to do both squat and deadlift every week. I try and ramp up the singles leading up to comp. Probably not sustainable long term though.

I am not sure I would want to throw in heavy singles in training like that. From my time working with coach Sheiko, he adds overload in the form of board press, block pulls, bands, and chains. I think this works better as it helps minimize technique breakdowns. If things feel good, I will add weight, but only if technique looks the same and bar speed remains constant.

I too have been implementing the heavy single before training for squat and bench once a week. But lately as volume accumulates I find sometimes I don't want to do it. I had a workout where I did a heavy single followed by a 4 x 2 and was very drained. It also affected my technique.

So I would play it by ear. I.e. if it is a low volume week and you are well recovered, do the single. If you are deep into fatigue, don't do it as it will likely hamper your workout. Also I would not go above 90%!

you can maybe employ a static hold with a heavy weight to feel the weight on your back/in your arms

What you could do is replace your Bench Press With Chains to slingshot bench, and add the weight of the chains at the top to the bar's weight w/ the slingshot. :D

It would be better to maybe add a few more high intensity singles into the competition period of the program, but I would avoid doing any extra overload work during the preparatory weeks, they are already hard enough, and adding more singles could mess with technique, and recovery, and risk injury more.