Hi Brandon,
Welcome to the family! You should be able to run the preamp out from the HK into one of the input pairs on the Zen, and experiment with running your phono stage directly into the other input pair vs., running it into the HK. We'll expect a full report

Be prepared to have the volume on the HK 50% higher to reach normal volumes when pairing it with the Zen amp, which is normal. In fact you can run the HK even higher on the volume dial by simply turning the volume on the Zen down. Your probably thinking "Why would I want to run the volume so damn high on the HK?" and the answer is that in general the higher the volume control is, the better the preamp section in the HK (or most things) will sound.
If possible during this time I would also connect a CD player, DAC, or IPAD with some lossless files, and see how that compares to the vinyl in both setups.
All this changing things up will help you to wrap your head around the amp.
The first thing you'll likely do when initially setting things up is find out what it takes to clip the amp and get used to the clipping characteristics of the amp. You'll know when it starts clipping because the meters will start to dance to the music. A little movement is no issue, but wildly dancing up and down will be easy to hear as the amplifier will be distorting. No worries, you can't hurt your speakers with this amp no matter what you do, and you can't hurt the amp either. It has neither enough power to blow up your speakers or itself. They last forever.
Steve