Ok, so regarding the last three days, for Thursday keep the same weight for close grip bench and try to get more reps, once you can get two sets of 10 you can move the weight up. Increase OHP by 5lbs. Do skull crushers this time, or some other tricep exercise like cable pushdowns, it you are failing at lockout you definitely need some tricep work. And maybe do DB rows on Friday instead.
On Friday, if the front squatting isn’t enough for you then you could do some paused front squats at the end, I don’t really like the idea of Anderson front squats but if you really want to do them you can.
For Saturday, increase the weight on t&g bench, try to do more reps with DB incline (aim for 12’s), and reduce the weight you are using for flys. If you aren’t feeling it in your chest then lower the weight slowly (like 5 sec. eccentric) and feel the tension in your pecs, focus on squeezing your pecs on the way up. Think “mind-muscle connection”, for compound lifts that is nonsense but on isolation exercises it is the way to get the most out of it. Also, since your Saturday workout looks pretty easy you could add a tricep exercise in there, the original intention was to do close grip incline but since that isn’t happening you could try JM presses. Do this after bench and DB bench, before flys, start with 3 sets of 10. It’s basically a close grip bench over your face/neck, technique isn’t as important since it’s not a competition lift but make sure to feel it in your triceps and not hurt yourself, keep your shoulder blades pulled together. Watch this video:
You say that you can handle more volume, if that’s the case then you can add one set to the 5x5 on the first three days (so 5x6 sets) and add a set to touch & go bench. Don’t go crazy adding sets to everything because you won’t make it far, remember that the plan is to increase weight every week (or reps if you can’t increase the weight yet) for 6 weeks, you can expect to be feeling some fatigue by then. The last thing you want to do is start off a training block with more volume than you can handle because you won’t be able to make any progress, you might build some muscle but the numbers won’t go up because you will be too fatigued to add weight to the bar. Also, keep in mind that you are training 6 days a week so each workout should feel like you could still do some more at the end.