I think I'd really like to see some photos - of both ends - so we can get some other opinions here. 3cm is a lot.
Are you absolutely convinced these are the perfect strings for you? Before modifying the instrument, I would personally spend some time trying other strings, that might fit better. But if you have already done that, and believe these are the only ones, then it may work out okay.
Moving the tailpiece further away will have no effect on the string tension. For the same string and tuning, the only thing that would affect tuning is the distance between the nut and bridge, which you are not changing.
The other potential concern is the break angle - the amount by which the string has to bend, as it goes from the tailpiece over the bridge. By moving the tailpiece further from the bridge, you will reduce the break angle. Again, 3cm is a lot, so it would help to see a photo of the bridge area, taken from the side, to get a better idea of how this angle would change.
Sometimes this topic is also discussed as down force, meaning how much the strings pull down on the bridge. Personally, I believe such discussions are often misleading (particularly as to the merits of running the strings through the body...).
However, you *do* need to consider how much angle will remain, as the string bends over the bridge, once you move the tailpiece. If there is not enough angle left, then the string may bounce around in the saddle somewhat, which would not be good.
I admire your willingness to modify the bass, to suit you. But it is a big step, so I encourage you to think about your string choice a little more before proceeding.
But with some photos, we may get some other helpful opinions, so post them when you get a chance.