I don't own an old DB with a great tone .
IMHO the reason to use a mic is if you have a nice sounding instrument.
Also as @jj.833 it's very challenging to use a mic in a live environment. The upright is not a very loud instrument acoustically compared to other instruments you are likely the work with. A microphone will focus on the loudest sound it hears. So if the sound of cymbals is louder at the mic capsule than the sound of the upright, the mic will pickup more cymbal than bass. Also if the sound coming from the amp is louder at the mic capsule than the acoustic sound of the bass, then the mic will feedback through the amp. Some people use a piezo for their amp and send the mic to the sound system.
In order to use a mic in a noisy environment, the mic must have a tight polar pattern and be brought very close to the bass. But using a mic this way may not sound very natural. First you are only picking up sound from a small part of the instrument, so you have to find a part of the instrument that produces a nice authentic tone. Another problem is most directional mics exhibit something called proximity effect. Proximity effect means that as the mic is brought close to the sound source, the frequency response changes; meaning the lows become emphasized.
One thing you can do is use gobos or sound shields to try and keep as much sound away from the mic as possible. Of course using gobos may be realistic in a well equipped recording studio, but it's typically not for live gig.
The bass specific mics that I can think of that work best are the Xlson Chuck Israel Signature mic, and the DPA 4099-B Core. But these are both expensive and have their limits in loud environments.
For the record, the only mic I ever seriously tried to work with was the AMT S25B. It sounded fabulous when just the bass played, but was unusable with an amp, even when mixed with a piezo contact pickup. I also felt the signal from the AMT picked up too much bleed from the drumset in a big band setting to be useable for the PA mix.
If your goal is to get a better arco tone I suggest trying the following: 1. Make sure your piezo pickup is plugged into something that provides an appropriate high impedance load. If the input impedance is too low, piezo pickups tend to produce a quacky sound in the upper mids that sound really awful with arco. The absolute lowest impedance is generally 1 Megohm. The optimum impedance varies with characteristics of the pickup. 2. Use EQ to smooth out the critical upper mids. Something like the Empress Para-EQ would be ideal, but even a graphic EQ pedal could be potentially helpful. 3. Choose and adjust your speaker so it works well with arco. Many 2-way bass speakers have uneven frequency response in the 2-4khz range. This range is critical for arco playing. If your cab has an adjustable tweeter, play some full range program material through the cab and try to adjust the tweeter to sound as natural as possible. You may find the tweeter needs to be rolled off a bit to eliminate phasing between the tweeter and woofer.
You are likely to find it is a matter of balancing out the frequency response of the bass, pickup, amp, speaker, and a utility EQ. The idea is no component in our signal chain is ideal, so you have to work out a compromise that allows them to work together to produce synergy. Achieving this is not necessarily an easy or intuitive task.
I don't think the KK BassMax is by any means ideal for arco, but you would probably be suprised how good you can make it sound if you address all of these issues. As an example, I used a Fishman BP100 for several years, and it sounded awful with Arco as well, but I was able to trick it into sound nice.
If you have not picked up on this fact,
@rickwolff has done a lot of experimenting with different mics. He has also posted a lot of video comparisons and reviews. I suggest searching through TalkBass using his user name. The image he uses for his avatar is the his Xlson Chuck Israel Signature mic. Perhaps he can suggest a low cost mic that will meet your needs.
If you have access to any decent mics that can be mounted on a stand, I suggest you do some experiments to confirm that a mic is going to give the desired results. In other words, don't buy a mic unless you can confirm it will actually be useful.