Now, I'm not as l33t as Cookiez, but I'm floating around the 800 mark atm in 1v1 so I should be able to help you.
The first thing that came to mind was that you have trouble multitasking, something that was illustrated multiple times throughout the game. You lost quite a few units simply because you were inattentive to volks grenade spam.
Personally, I never go LT anymore unless I'm supremely confident I can end the game with the AAHT. I'd also recommend switching Armor for Infantry Company as Cookiez wrote an excellent guide for using it
here. On maps like Langres that are wide open, the M1919A6 will greatly help your riflemen scale into late game well as well as mitigating the 'nade volleys with the suppression granted by defensive stance.
Your LT opening left you pretty vulnerable to the OKW AAHT which is the reason why I barely use the LT tier anymore. You used your own AAHT well until you lost it to the Puma in a ballsy rush to destroy the OKW Flak HT. Again, Captain + Stuart would have shut him down from the get go and the 1919 would cover any gaps in your ai firepower.
You did manage to destroy his AAHT when he retreaded his volks, good job, that took a lot of pressure off of you. Unfortunately, you chose to wait on the E8 call-in. This isn't the Red Army, your regular M4A3 Sherman is more than capable of dealing with just about everything OKW has, even the Panther (rear armor shots). I have no problem with getting one E8 as a spearhead tank, as it can take more punishment, but a couple of stock Shermans would have ended the game much quicker. Their HE shells are nasty against infantry and can also deal damage to light vehicles.
You also produced FIVE E8's. Now that is a veritable ass ton of fuel wasted imho. Just some quick math here, Major is 90 fuel, regular M4A3 is 110, and the E8 is 145. So with your 5 E8's, that's 725 fuel on a frankly mediocre tank. For that amount of fuel you could have gotten the Major (and a forward retreat point) and 5.7 M4A3's. That's almost 6 Shermans and a Major for the same price as those E8's.
Why the economic rant? Because you never needed the E8 that whole game. When the Panther came out, you had two AT guns ready and frankly if you had just used M4A3's instead, the game would have probably never lasted that long. The M4 is an excellent squad wiping machine. Instead, you fiddled around with the E8, but they failed to make much of an impact, even when you had 3. Those volks/ raketenwerfers would have never been able to stand up to 3 HE Shermans for anywhere near that length of time without getting wiped off the face of the planet.
This brings me to yet another point. You make the same mistake I've seen others do and I wonder at it's origin. At one point, your tanks were taking fire from a Raketen, but instead of moving out of its cone of fire and flanking/wiping it, your tanks just sat there. I don't understand. You're taking fire, so the natural reaction would be to move, right? Medium tanks are excellent at flanking as they have great mobility, so there's no real point to just sitting there and letting them take free shots. Yes, you did wipe it, but you want to maximize the amount of time your armor is on the field instead of at the repair shop.
The OKW player made the massive mistake of not getting a Medic Truck until ~30:00 which really gave you the advantage in terms of attrition. Your medics kept your men fit and your flamers were racking up kills like credit card numbers. In addition, you saw the OKW player use his Stuka zu Fuss. That should have been an immediate green light to rush an M4A3 since you now know he won't be getting any real armor any time soon.
Also, if you manage to push your opponent off the field and have excess MP, throw down a fuel cache. That's how you prevent comebacks.
The USF requires a late game combined arms approach more than any other faction I'd say. They don't have LMG42 Grenadiers, Shocks/Guards, or Obers and unless you go for Airborne, the humble Rifleman is your only infantry unit all game.
This is why I'm such a proponent of the M4A3, it's a truly amazing tank with its versatility. I used to think that the E8 was the best tank the US had, until I had my eyes opened by how the much cheaper stock Sherman was frankly a lot better in terms of the combined arms approach. It excelled at wiping out entrenched infantry and accompanying rifles could easily deal with any AT guns/ shattered remnants of your enemy's forces.
Again, I have no issues with using one E8, but more is a mistake imho.
Sorry for the long rant, but I've seen so many players throw away the game with their expensive Easy Eights when with a bit of additional micro the more combined-arms oriented M4A3 quite frankly outperforms it.
I'm sure Cookiez will cover what I missed. I hope this helps.