So for awhile now I've been doing an Upper/Lower 4 day split. I kind of modeled it after the BBB template on 5/3/1. It's working well, and I am enjoying the length of the workouts.

So Bench/Row heavy, Squat heavy, rest, OHP/Chin heavy, Deadlift heavy. Then do the opposing day as assistance (So Bench heavy then OHP 3x10, or vice versa), and the main lifts I've been doing at 3x5 since progress is still steady for the most part.

However, I'm basically like the tin man. Even with a hot shower, and a good chunk of active warm up before warm up sets, along with stretching between warm up sets, I still never really get loosened up until some working sets, I could warm up for 45 minutes and still be tight. It has been this way since I was young even, playing sports in high school and college was the same way. The warmups did a little bit, but things didn't start to shake loose until we got right into the harder drills.

So when I am on a Push/Pull set up, or full body, my second lift of the day is always the strongest. Squatting first leaves me feeling better for bench, benching first will help with squatting. Not sure why, it just happens that way.

So instead of jumping right into the warmup routine for say Deadlifts on the heavy deadlift day. Do you think it would be counter productive to warm up to my 3x10 Squat sets, complete them, and then jump into the warm up for the deadlift, and opposite for Squat day?

Obviously I wouldn't skimp on any warm up or try to replace the ramping sets up to the main lifts. I don't think the 3x10 sets are intense enough to affect much on the next lift, as far as stamina in the tank and fatigue for keeping proper form.

I am going to give it a shot the next workout, but just thought I would get input first.

You are over thinking it.

just thinking aloud here.
what if you did some high rep but slow it way down and increase time under tension. That should get some blood flowing to the areas and maybe get things going?

Most likely.

I might just need to increase the reps on the lighter warmup sets. I stick close to the 5 warmup set scheme for 5 reps. 2x45, 1x40%, 1x60%, 1x80% then working weight for the day. And despite what a lot of sites say, I'll do some static stretching in between a few warm up sets, especially the hamstrings and back.

Look up post activation potentiation