New one not for sure. And secondhand as well.

Otherwise you would be 900-1000+ EUR for secondhand device.... Say Fireface 802. If you could use firewire, even older Fireface 800 might work. But, probably it is better to raise the budget.

I would recomend to buy RME interface that has RoomEQ. It is quite probable that if you buy older/cheaper solution, you will miss it sooner or later and regret that you have not invested more right away....

EDIT.
The following was wrong, I thought expansion has 6 channels, but it has only 4. So, 6 in total...

Maybe something like PCIe card HDSPe AIO and expansion card with outputs. If you are lucky...

Probably Fireface 802 FS, if you want also 8 analog ballanced outputs.

See my interface comparison sheet: https://forum.rme-audio.de/viewtopic.php?id=35156

Products with RoomEQ and 8 analog outputs, for max 600 € .. sorry, impossible.

Models that meet your requirements:

- Current models
       USB2: 802 FS, UFX II
       USB3: UFX III
- Additionally, from the used market:
      USB3/TB: UFX+

Even when buying an 802 FS from the used market, the price will be much higher than €600.
The 802 FS is a model from 2023, so the price will be in the range of 75% of the street price: €1599 * 0.75 = €1119.

I bet in most cases you have more often hissing coming from active monitors than actually from the recording interface.
What is high dynamic range, when does it start for you?
You won't hear this high dynamic anyway without blasting your ears.
The usual listening levels / work levels to not ruin your ears after hours of work are much below your SNR/DR expectations and what those devices nowadays deliver.

To stay in budget with new devices you would need something like Digiface USB in combination with Behringer ADA8200:
€425 + €159 = €584

But then you do not have RoomEQ and the RME conversion quality.
Also useful things like a few Mic/Inst inputs and Word Clock wouldn't be part of the setup.

Even when it's over budget I would go for an 802 FS, UFX II or UFX+ from used market.
Expect prices around 70-80% of street price depending on age and condition, due to quality and long firmware and driver support.
Then you have RoomEQ, excellent RME converters and many useful features on top.

Just as an information. 802 FS and later models of the UFX II (starting with 2023) have the same analog I/O board (except Mic/Inst inputs) like the UFX III (since 2023) with AKM 4490 converters, that are known from the reference converter series ADI-2 Pro [FS].