How much do I need to spend to make vinyl sound better than digital?

The issues you describe sound like it could be a less-than-optimized set-up.

My guess is that if you haven’t spent the time to fine-tune your table set up, then that’s where I’d start. Now, perhaps your particular model doesn’t allow for much fine-tuning, which would be a related issue. Nevertheless, if your cartridge isn’t perfectly aligned and sorted out together with your arm and table, then you’re not hearing what your rig is capable of.

I’d start there.

You’ll learn more about how it all fits and works together. There are various tools that can aid you. Do all that before investing in a new anything. Then, from there make a call.

Vinyl is an incredible medium but it takes work to optimize it.

These results are inevitably some combination of: 

• You might simply prefer the tyically "clean" sound of digital
• The kind of music material you enjoy has generally good mastering quality on digital; at level with or better than the vinyl alternatives
  • I enjoy a lot of 60 - 80s pop & rock - and this material fares much better on vinyl, IMO (on average)
  • Some of the 1990s+ Redbook CDs I have from Japan sound just as good as vinyl
• Poor isolation. A good headphone setup can reveal if that’s the problem or not!
• Your analog rig might not be that great. It could be one weak link in the chain, multiple pieces, or a bad match between anything. That said, if the above factors don’t swing you to vinyl, then there’s little point in spending gobs of time & money to improve your vinyl chain. 

And yet another opportunity for one of my favorites:

Typically, these days you can equal things by carefully choosing and investing about the same amount as your analog rig. For me my digital and analog sound simply stunning and the same... as I desired. You can see my systems under my userID.

For systems that are more budget oriented, sometimes you may need to spend a little more on digital... say maybe up to 20%. But this is changing rapidly. 

So roughly: Turntable + Phonostage = Streamer + DAC. 

You have to put the same effort you would into choosing a TT, cartridge and phonostage into the Streamer and DAC. My rough rule of thumb for a digital system is 30% speakers, 15% amp, 15% preamp, 15% DAC, and 15% streamer, 10% cables and interconnects. Really generally. Same for analog 15% TT and 15% phonostage. 

It can't be done. You could spend $100K on the most esoteric turntable, cartridge, tonearm, base, cables, and phono stage, and its potential sound quality will never equal that of spending $10K on a network player/streamer and DAC. It just is what it is.