may carefully dig into it and reconnect cells for 12v use
OH FFS NO, don't do that. You will wreck the panel.
Get an MPPT charge controller. They allow the panel voltage to be way above the battery voltage, they are much more efficient any way. Depending on the model, they could charge a 12 volt battery from up to 80, 120 or even 150 volts panel array, though they are most efficient when panel array nominal voltage is roughly double the battery voltage.
100w panels are so small they are barely worth the effort and hardware to install them these days. I don't know the situation in the USA, but here you can get second hand solar panels for almost scrap value very easily. They are all over Gumtree for example. My last collection was 8 x 200 watt Trina panels for (from memory) AU$200 the lot including the mounting frames and clamps. That's 1600 watts of panels for about USD$135. They had been removed because the home owner was upgrading from a 1600 watt system to a 6600 watt installation. People want the cells on the roof to all match these days to look nice, so they don't add to existing systems, they replace small systems with big systems. If you are prepared to go out and collect used decommissioned panels, they are absolute bargains.
I digress - MPPT regulators allow you to have a 24 volt panel system charging a 12 volt battery. The internal electronics match up the voltages. That's similar to what I have - 3600 watts of PV panels, nominally they are pairs of 24 volt panels in series, so nominally a 48 volt PV array charging a 24 volt bank of batteries through two MPPT regulators, an older Apollo Solar 80 amp regulator and the newer addition, a Victron 70 amp Blue Smart regulator.
There are cheaper ones around, I believe Renogy and Epever are good quality cheap brands of MPPT regulator.
I say "nominally" because in good sun, panel voltages run way higher than the rated voltage - My "48 volt" arrays run at 65 to 75 volts in good sun, the MPPT regulators allow the panel voltage to go that high for better efficiency.
My batteries are getting on now, they were new in 2006. They are Exide Energystore 2 volt 1330 Amp/Hour lead-acid cells, a bank of 12 cells to make a 24 volt system. I look after them well and they still perform like new as far as I can tell. They do need to have distilled water topped up every month, but I have a home distiller I bought on Ebay so I brew my own distilled water using surplus power on sunny days and stock it up over summer. I distill rainwater so it's all free. I very rarely let them get below 90% charge, they have NEVER been below 85% charged. That's right, lead acid cells should only operate on the top 10% charge to get a good long life. So a 200 amp/hour battery should never have more than 20 amp/hours taken out. The lower you discharge them, the shorter the life and it gets dramatic below about 60%. My first set were 15 years old when I got them and we got another 15 years, 30 years is a great life but they were pampered. My current ones were bought new in 2006, I hope to get 20 to 25 years from them. Then I will compare lithium and lead acid, plus any other technologies that may be around by then.
I suggest you watch some Youtubes on solar MPPT regulators. Will Prowse has some good ones, he has made an absolute fortune as an online solar guru. He expresses himself clearly and gets his point across well.
He is absolutely gorgeous, so that is a bonus, too.
There are quite a few used panels avalible,but they are far from me and " local pickup only"My setup is quite small,so 100w is useful-gets about 6a charge 
