I am no expert, but I thought I would provide you with some "food for thought." 18611 seems like an unusual battery size to me. But, 18650 is extremely common and probably very close in size (4mm longer?), so I think you can easily get two good cells to replace your dead cells. ("18" refers to 18mm diameter, and "650" refers to 65mm length. So, I think your dead cells are likely to be essentially the same size, only 4 mm shorter. I suggest that you measure your cells and see what size they actually are.)
The new cells that you purchase are not going to be cheap. However, they are likely to have much greater capacity than 700mAh. (I think around 3000mAh is pretty standard for 18650s these days.)
I believe, however, you may have a problem with connecting the bare wires at the end of your connector to the cells, and with the metal connector to "bridge" the two cells at the opposite end. The problem is that, as I understand it, you do not really want to solder that connection. Soldering involves getting both the cell and the wire hot enough to melt the solder. I believe heating the cell up to that temperature is bad for the cell, and may also be dangerous. The preferred technique is spot welding. Spot welding is so quick that the cell doesn't have time to heat up very much. However, most people do not have access to such spot welding equipment.
On the other hand, I believe that many Remote Controlled vehicle enthusiasts make their own "battery packs" from individual cells. So, you may be able to find out how they are doing it, and use whatever method they use. If you have enough space, you could also consider using a two cell battery holder. If you are able to use such a holder (many of them are reasonably small), then you would not have to worry about making any kind of permanent connection directly with the cells. (If space is an issue, but you wanted to use a battery holder, you might consider using smaller cells such as 14500 which would provide the same voltage, but with less mAh capacity.) One significant advantage of the battery holder would be that the cells could be easily removed and used for other purposes, should the need arise.
In any case, I believe you have come to the right place. I am confident that others on this forum can give you better and more thorough advice.
