I can get the side panels off by lifting them up and rearward. I have only one 1000-CCA battery on the righthand side. But I know what you mean. Even with the boom up and panel removed I still have to take off the longish body extension that locates the side panel. I still pay hell getting it out---I use a closed-end wrench slid over each the terminal and then lift them like offset handles. And the battery is HEAVVVVY too. Something to look for is the terminals that NH uses have a center bolt through the cable--it tends to loosen and makes it near impossible to charge AND start it under the right conditions.
As far as getting the boom up manually, my machine uses a bunch of electronic controls that won't allow the hydraulics to lift but I can get it to go down doing as you described. The only way I know is to use another machine to lift the boom and release the back pressure like you did. Luckily I had my backhoe handy to lift my boom. In a pinch without another machine, you could jack up and block the rear of the machine to keep it from tipping backward, then use a jack under the boom/bucket to raise the boom (relieving the backpressure of course otherwise it will just lift the front of the machine eventually). You would have to contiue raising and blocking the boom/bucket until you get it high enough. You could also lift the rear of the boom at the square tube loader arm crossmember that is over the radiator/rear of the machine. Harbor Freight has a 10- or a 20-ton porta-power that comes with extensions and different end configurations to suit many needs---think of a skinny bottle jack with a remote hand pump and long neck extensions (about $100). But again, you will have to relieve backpressure otherwise you'll end up lifting the entire rear of the machine. I use my 20-ton porta-power with a modified pull-back cylinder (versus the typical push-type cylinder) to install my steel tracks and adjust them. Cuts installation and adjustment time down to minutes versus an hour with ratchet straps.