Low B with a standard "low E" 4 string set

[Shoewreck]

I've been wanting a low B for a long time. Today I tried tuning my bass stringed with DR hi-beams .045-.105 5 steps down. I played a couple of songs on rehearsal, then tuned back up.
I've appreciated the tone and even the floppiness - it brought lots of growl! Nice slap (it felt like squishing frogs - don't blame me, I've never actually killed one!). Have I mentioned the gut-shaking low B and ability to play low in higher positions?
The problems were:
1) wrong intonation on E (former A) string
2) wrong notes caused by unusual tuning
3) hard to tune

It's time to buy a new set of strings and I'm looking for 5-steps-downtuneable set. What would you suggest? I've read a lot about much higher tension of flats. I don't mind flats because I hate the zing. I don't want to go for a 5-string set (throwing away the first one) because I'd like to stay with unmodified nut.
I'd probably go for one of these sets:
.110 or .105 D'Addario Chromes
.110 or .105 D'Addario Half Rounds (I had a .110 set tuned to low E - it was hard as a solid rail, the set is currently gone, so I can't try it back)
.110 or .105 La Bella flats
It may also be GHS half rounds, but I'm not sure they're available (not too many brands to choose from, because I'm living in Russia).

I can play lighter to control floppy strings and I dig the tone. I just don't want to go over the border.

[sir juice]

buy a 5 string

[Shoewreck]

Buying a 5-string isn't the most cost-effective solution. And I don't want to mess with different string spacing and neck size. Even switching from one 4-string to another took me a couple of months to feel comfortable.

Let me put my question shorter: which set of strings is the most stiff and tense?

[dman_113]

I used .110's tuned into drop c and they worked quite well, I believe they were Fodera's.

[Stay Gold 1337]

i think ernie ball make a set with a 110 in it for 4 string

[Roland777]

You could try saitenkatalog.de, get singles from there. Buy D'addario-singles en bulk and you'll save cash compared to getting sets - I know I do. Props on making .100-area-strings working at B. Lowest I've gone is a .105 to C. I'd probably go singles in .115-.090-.065-.050.

[meev992]

I was able to use D'addario XLs, .110 E tuned to C. I assume that .115 roundwound would be just enough to make it to B, with that same, detuned/loose feel.