If you have a 95 amp alternator, you're getting close to break-even on charging with a lot of accessories running at once. I started with a stock 95 amp, and with high beams, blower on high, and wipers, I noticed the turn signals barely blinked, I mean, slowly, and this is at idle. That means the alternator is not keeping up.
Now, I'm in Northern MN, and this combination of accessories is pretty much the way it is most of winter, and looking at your pictures, you are in a similar situation.
I would do the following, in order, and you may not need to do all of them to get where you want to be, but none of it is difficult or expensive. And, I'm just thinking... if you did this first, you would have better performance from the stock headlights, and maybe not even need the aux lights. Anyway, I would suggest the following in order of expected improvement:
1) Your headlights appear to be glazed over. If you can't look in and see the bulb clearly, the light is going to be scattered coming out. A new pair of headlight housings runs about $60 on
Amazon.
2) There is an aspect of the wiring in 1st gen explorers that reduces the brightness of the headlights. Power for the headlights has to go through a lot of relatively thin wire, through the headlight switch, through the low/high beam switch and then out to the headlights. There is a lot of voltage loss in that path. What you would like is a harness that uses relays and bigger wire to get the best voltage you can to the headlights. Now, here is a harness from
LMC trucks. BUT, for some reason, there is an issue with daylight running lights, which I think might apply to you. But, hopefully you get the idea.
3) If you don't have a 130 Amp alternator, I'd get one. If you look at pictures of the 95 Amp vs the 130 Amp, you will be able to tell which you have. The diameter is noticeably larger on the 130 Amp. But, they are completely swappable, the bolt pattern, belt and connections are the same.
4) Everything so far is pretty basic. If you want to go the extra mile, then you have to address another issue. All alternators have low output at idle. So, you can improve that by using a smaller pulley on the alternator.
I think this is the right one, but if you do this, please call them and verify it. You will need a slightly shorter serpentine belt to go with this. Vehicles manufactured to be police cars run this mod because they sit and idle so much.
Other stuff - If you run the aux lights, I'd run them off the battery with an in-line switch, and again, relatively large wire. Also, for what it's worth, I tried Bosch off-road high output bulbs. They helped but they burned out too quickly to be practical.
Anyway, good luck!