Appropriate gauges?

You can likely use the nut you have. I believe you will find tonal benefit from the tension relationships you put together and am looking forward to your take on it once you do this.

If you have the budget, having a balanced set for comparison/backup may be prudent.

 

I would think you would want it similar, or even a slight bias in tension towards the C string. This is because the more mass to the string will start to damp the string's overtones, so over time the heavier E string will not be as bright or even toned as the C string. Classical solo double bassists prefer even tension across the board, as opposed to heavier lower strings for section use.

Something like the new balanced set D'Addario EXL-220BT 40-55-70-95, plus a .030 for a C string sounds like it will do what you are wanting to do right now. XL's tend to be twangy, but they settle in with good, almost "scooped" clarity, which may be exactly what you're looking for.

 

I use Circle K matched tension strings. I happen to like about 40 lbs tension per string, but their chart makes it real easy to pick lighter gauged strings in a lower matched tension too.

 

I do something similar, but definitely not that light!

I use custom sets from Bass Strings Online, I like being able to choose the gauges I want plus not being stuck with one type of string. He has a huge selection of different types and makes that you can make custom sets with:

http://www.bassstringsonline.com/Build-your-own-string-set_c_163.html

If you want something you can play with a light touch, I highly recommend round core strings. Look at DR...HiBeams for steel or Sunbeams for nickel. The round cores make them super responsive and effortless to play.

 

Assuming all other things equal, more tension means that the string is less flexible, so a greater percentage of the energy is transferred into vibrations of the harmonics and less to the fundamental frequency. This means that the higher-tension string will be a bit brighter and clearer, but the lower-tension string will be a bit fatter and bassier.

Although more extreme, try detuning your G-string down to D and play it along side your open D-string. This should give you an idea of the role tension plays in tone.

 

Through years of experimentation i have discovered that tension falling from low to high is perfect for alternative techniques such as chords, tapping, fingerstyle, string bending. So your set is ideal for you, it will work better than an 'equal tensions' set. In fact my recommended gauges for other brands are very close: .095 .070 .050 .035 .025. Make sure to build a custom set from singles, there are no inverted tension sets available at the moment, despite the many advantages, CKS singles come at no cost penalty compared to the sets.
You very probably will not need a new nut, i have been using a .040 in a .165 slot and a .007 in a .032 slot with no problems, as long as the nut floor has a curve the downforce at the nut keeps the string centered just as well as fretting with a finger would.

The .030 is tighter than the .040, which itself is too tight for someone with a light touch who wants to use advanced and guitar techniques.

 

OK, then, maybe a .028. D'Addario has a tension guide that can sort that out.

It is my experience that the higher gauges, especially on the E string, have damped out with less overtone response than smaller gauges, over my 38+ years of playing bass. YMMV.

 

I think a big part of that is in construction technique. String manufacturers will often make the E-string stiffer (I think D'Addario uses a 3-wrap?) so that it can stay at a lower tension and still feel somewhat consistent with the other strings.