Being an upright player for most of my life and playing both acoustic and EUB’s I understand your desire to get a more acoustic tone out of an electric instrument, nothing beats the sound of a well miked acoustic bass. In my personal experience an acoustic tone is just not possible with an EUB. I have tried multiple pickups and have managed to get some great tones out of EUB’s but nothing like what an acoustic bass sounds like to your ear. Even if you have a resonating hollow body EUB like an Eminence, once you use a pickup you lose any chance of getting a pure acoustic tone. If someone can prove me wrong I would be extremely happy to be mistaken about this. The only thing I can think of that might possibly work is modeling but I’m not aware of that technology for upright bass.
Even an acoustic bass doesn’t really sound like itself when you put a pickup on it and put it through an amp. A piezo or magnetic pickup can potentially get you a great amplified sound but it still is electronic and lacks that beautiful natural woody sound that the bass creates as it moves air. Side note, using a preamp is very important in order to get a good amplified tone by buffering the extremely high impedance of piezo pickups. Whether I play my acoustic or an EUB live what I go for is a warm, fat, articulate tone more than trying to match the acoustic sound. I suppose you can experiment with some short delays or reverbs to try and replicate the resonance of a bass body with an EUB, I personally haven’t tried that.
I listened to your track and your bass sounds quite good. Is it an NS? One suggestion I have is dial back the high mids, around 1K or so. Those frequencies are always too strong with any kind of upright bass pickup, acoustic or EUB. Piezos emphasize that high mid nasal growly string noise sound which is a part of a natural bass sound too strongly. I haven’t tried the NS strings (but I do use D’Addario’s, they make them) so I can’t offer an opinion on them but I’m guessing they will give a good warm tone but not sound significantly more like an acoustic. Remember, the pickup is just getting either string or bridge vibrations so changing strings will change the sound somewhat but not the character of the instrument.
Here is a link to a video with my EUB. The bass itself is a one off, an Ampeg Baby Bass neck with a mahogany body I designed. It has a Wilson pickup, Sadowsky preamp and D'Addario Helicore hybrid strings. I’m not on camera much and only walk, no bass solo but I’m posting to demonstrate that if I can get this kind of a sound out of an EUB (I can’t travel with my acoustic) I’m satisfied.
Bottom line, unless you’re going to get an acoustic and a good mic and run it through a PA (which can be very problematic in a band situation) just go for a good warm, punchy and clear tone with your EUB that supports the music you’re playing and is pleasing to the ear. If you come across a way to make it sound more like a real acoustic please let me know!