Okay I saw the link missed it the first time. I had a few of those speakers on that list.

The OP's Yamaha N-1 speakers are especially highly regarded.

Personally if these (OP) speakers aren't having any issues to speak of I would keep them. I am not sure the speakers available for under a Grand would be a slam dunk. YMMV.

I did pick up a pair of Polk Reserve 200 Anniversary edition recently and so far my findings - these are an excellent speaker for the $$.

Unless @lukasread only wants to playback vinyl I still like the addition of adding a streamer. So much music that I wouldn't even been aware of I am now enjoying. It used to be the radio that was the source for new music, now (for me) it is streaming. Plus it sounds really good!

Other than that a suggestion of a new cartridge is also a great idea. 

Cheers 

new amp the vintage pioneer will not have the clarity of a modern amplifier

@dougsat I agree it's a tough question from a small budget. But not impossible. I have been spending $3-500 a year and have made improvements.

1st Post, Welcome Aboard!

I would keep

Pioneer Receiver

Pioneer Speakers (level controls, yeah!)

sell Yamaha Speakers or use elsewhere or give away

New Cartridge with Headshell, Your tonearm has a removable Headshell, plan on moving the new cartridge to a better Turntable later so the improvement/investment is transferrable

My favorite not very expensive Moving Magnet Cartridge (works with your receiver’s phono input) is:

Audio Technica Headshell/Cartridge Combo Kit

VM540ML/H

includes a headshell (keep your old cartridge/headshell/factory aligned) for when you get a better turntable you can put the current one back on, sell old TT or use elsewhere or give away).

It has a MICROLINE Stylus shape, much better sound and lasts longer than others.

Adjust the level controls of those speakers for your listening space.

How old are your ears?

I cannot post links, but you can find and read this article

sound-smith dot com /articles/stylus-shape-information

Speakers often have the most impact on the system. Find something you love that works well in your room, and that can be driven by your amp.  Lots of great deals on used speakers in most markets. 

A cart upgrade is a never a bad idea! 😎