Looking for upgrade from Apple TV, would like to keep using iTunes and wifi

My wifi-based sound has never matched my dear departed Arcam Alpha 9 CD player.  I've read forum after forum but I don't see a simple solution.  One possibility is that an audible problem occurs when the bit rate is changed from the CD native 44.1 kHz bit rate to the more traditional 48 kHz.

Here is my wifi system: iMac (iTunes) -> wifi -> Apple TV -> optical TOS -> PS Audio Digital Link DAC. 

The 300GB of music has been ripped from CD and is stored using Apple Lossless compression.

Yes, I know it's a lot of Apple software and gear.  I want to keep the iMac and iTunes and the wifi link.  I like the playlist features of iTunes, including the Genius feature. 

The Apple TV comes with a remote control and I can access the iTunes playlists directly, using my TV as a monitor, even though the iMac is in a separate room.  Once the playlist is playing I turn off the TV.

I am an electrical engineer and I've even worked measuring jitter on serial bit streams.  I understand that converting from 44.1 kHz to 48 kHz will cause some sort of interpolation error whereas converting from 48 kHz to 96kHz can be done with no trouble.  However, the Apple TV outputs 48 kHz so the bit rate must have been changed somewhere along the chain.  My PS Audio DAC won't even lock to the native CD rate of 44.1 kHz.

Are there any suggestions for a wifi receiver and DAC that will match the sound of a good/great CD player?  The budget is about $600, with an upper limit of $1000.

There's always issues doing sample rate conversion it's not as simple as saying that 2x is going to be better than 1.8x.  Some algorithms are better sounding than others though.

I'm not sure I understand the problem with your DAC though, 44.1 should be easy for any DAC.

Wyred4Sound Remedy is an asynch. sample rate converter and it samples everything to 96/24, around $300-$400 new depending on the sales.  I have one, and used it for a couple of months, works peachy.

Are you willing to change to a local music server? Then you could use USB 2.0 to feed  your DAC which is often the superior connection.  I built a Linux server for $600 and got Web, Android and iPhone apps. :) I have it feeding a USB 3.0 hub, which is then connected to my DAC, but there also an optical output.  Double check your DAC is USB 2.0 and driverless on Linux. If it is, then you are all set.
Wifi through Apple TV and optical to the dac does not sound very good.  No idea why not, but it doesn't.  You will have much better results doing a usb connection direct to the dac.  The cheapest option is to buy a Mac Mini and use it as a dedicated server, if you are sold on iTunes etc.  It also allows you to use third party software like Pure Music or similar, which will not work over wifi.

It does not have to be dedicated when using network (USB, WiFi, Ethernet etc) since computer timing is irrelevant.  I use computer for other tasks while playing music over WiFi.

While 48kHz to 96kHz conversion is easy (PLL - even ratio) 44.1kHz has to be interpolated to 48kHz and it won't be accurate because frequencies are too close.  I'm surprised that your DAC would not work with 44.1kHz - a basic frequency of CD.  

I use WiFi with Airport Express and jitter suppressing DAC.  Adding jitter suppressing async. rate converter like  Wyred4Sound Remedy,  as suggested by eric_squires, is a good solution.  It won't fix your 44.1/48 problem, but will make your DAC less sensitive to jitter (that converts to noise on analog side).

Airport Express is very basic but there might be better choices.  You could also switch to async. USB DAC or USB/Spdif converter. Async USB DAC receives music as data in packets.  New timing is added with low jitter internal DAC's clock. Computer timing becomes irrelevant.

I'm afraid there's some misconception. Interpolation is the process of mathematically guessing missing samples. It is still interpolation if the new sample rate is 2x or 2.18 and there will still be precision issues. The latest rate converters can handle either equally well.  Whether that is good enough or not is another story.  Music is rarely that linear, so guessing a sample between to adjacent samples, even if dead in between, is still guesswork.

There are some advanced algorithms which use splines, but rarely do manufacturers disclose what they are doing.  Wadia was a rare exception, but it was their claim to fame.  At least if you use Linux you can find some of these and apply them to do SRC for you.