I've been marching and playing for 45+ years. I play lead trumpet, but also first soprano with a small drum corps. Sometimes, I'm the only lead that shows up and I have no problems.
Many times people will swear that you need lots of air and the truth is; you don't. It is more important how you use your air. Playing in the upper register is unique and someone that cannot play for hours in that manner truly has no idea what it takes.
You are playing lead now, so obviously, you have some talent in this area already, but maybe need some ideas for improvement in how you do it. Maybe some of my ideas will help.
You need to experiment to see what works for you. There are many methods to try and some personal variation will work for you, but it is not instantaneous or easy. There is no magic bullet; "do this, and you'll be hitting double C's all night."
Lastly, but just as important is equipment. It must be a good fit to how you play to get the best results. Many people assume that the horn/mouthpiece plays only a small part in the ability to play lead. In my opinion, they are dead wrong.
You need to find the SMALLEST mouthpiece you can comfortably play on. Notice I did NOT say the shallowest. Many people work too hard trying to use a mouthpiece that is just too large for them. A shallow mouthpiece might help your range and endurance, but usually makes everything else harder, so it is not a "cheater" solution. One way or another the hard work is always there...no free ride.
The fact that you end up using a lot of pressure indicates that you need to strengthen your chops and find appropriate equipment. There are all sorts of methods to strengthen the muscles of the mouth. Try that right away and do it a lot.
Next experiment with tongue arching, and with minor changes to your embouchure to see if one of the methods you see on the internet may work for you. Speeding up the air stream with a tongue arch does work, but there is so much more you can do with a little research on your part to see what has worked for others and just try it. Most lead players are only too happy to help.
There's another method which seems to work miracles for some, but it escapes me, and it's called Tongue Controlled Embouchure or TCE.
Many people that use a lot of pressure when they play are working against forces that keep their lips buzzing. You may be someone that needs a certain amount of resistance, more than some, to keep your lips buzzing. I don't recommend a small bore horn, but I do recommend a medium to large bore horn with a tight backbore on your mouthpiece, along with the smaller rim diameter and a comfortable depth cup. (I like the Curry 600 series for lead work).
I would also avoid mouthpiece rims that have a sharp bite or high crown such as a Bach. Marching and playing lead on a Bach, even with a wide rim, is almost like playing a meat slicer. Although for classical playing in a concert setting Bach mouthpieces are fine and produce a wonderful tone and easy articulation.
These are just some of my ideas to give you a direction. For you, and maybe some others, you may find just what you need in what I've said. For some, that agree with none of it, it will be total bs and I'm sure they'll say so. But listen to all ideas, that seem reasonable and improvement may not be immediate, but if something works for you, you almost certainly will sense it right away and that's the way you want to go.
The longer you play at a time, you will inevitably end up using pressure to compensate for tired chops. Even after you have success learning how to play lead without much pressure. If it's a paying gig, you may have no choice, but if it's not, then stop before you hurt yourself. Take a break and use some ice, if it's available, to reduce swelling - for just a little while, though.
Hope this helps and good luck to you.