you can try contacting Damien Johnson in the UK, he runs "Q Washers" services in the UK, hes the king of anything pressure washers as far as fittings, custom setups, hoses, etc... Ive bought from him in the past back when i had a Karcher pw. His email:
[email protected] He usually responds within a day or two. Just be very specific on what your looking for and he may be able to help.
To me the stock hose end for the spx3001 looks very similar to the Karcher K-series hose end fitting, see pics below. There is a notch on the Karcher fitting which may effect the seal when the hose is plugged into the SunJoe hose reel receptacle... i just don't know. We would need a guinea pig to try it out.
*EDIT* I just did a quick search through Damien's listings and found this...
KARCHER K SERIES HOSE 20M SCREW FITTING 22MM FEMALE X MALE GUN Q RELEASE PROBE | eBay