Good friend of ours has a 48ft Princess in Chi, he feels the same about East Head. Point is do you want to sit at anchor with some nutter in a sports boat using you as a turning marker as your anchor drags?
Assuming Snowleopard means the pool opposite CYB, there is plenty of water there and further up at any state of tide, but dont get too close to the bank as it does shoal. No moorings above the entrance to Birdham Pool, until you reach Dell Quay which is drying, although worth a visit at HW (good pub - the Crown and Anchor) and lie alongside the jetty for about 4 hrs round HW. Dont anchor for the night much above Copperas buoy and not in the bay west of it, as it dries, and keep to the West of the 2 beacons marking the entrance to CYB and Birdham - anywhere East dries.
Other possible places: top of the list Pilsey - above the 2 marker posts in the Thorney channel is much quieter than Pilsey itself for some reason. Again no moorings. There is a recommended anchorage downstream of the Itchenor moorings on the south side, below where the Bosham channel joins, but I never used it. Again plenty of water at all states of tide. There are several 'Rythes' or creeks coming off the east side of Hayling which provide varying degrees of shelter in settled weather, which are worth checking out.
Then East Head - the 'famous' Chi anchorage. beats me why its so popular other than the sandy beach for the kids. Poor holding, shoaling in many places, right on the main channel down from Itchenor, exposed to SW wind (unless you tuck righ inshore where theres no water). And at busy times packed out. It can get quite amusing when the tide turns on a fresh breeze and anchored boats swing at different rates according to their windage! Add a couple of dinghy fleets racing through the anchorage..... If you really like picnicking on the M25, then E head is for you.
Anchor at east head for a day on the beach, the holding is some sand/mud but big stress loads of boats and watch the shoaling sand to the east of the beach, anchor trips when the tide turns at 3am for the pyjama dance.
Emsworth channel is good mud holding and peaceful
Or on the east side in the Chichester channel on way to 1KM NE of east head itchenor. or as has been said Pilsey.
For more peace of mind the option of Mooring bouys - Itchenor (beware the crap food and rude staff in the ship).
Off Sparkes just past entrance,
Emsworth Channel visitors or empty (most of the white ones at the end of channel are deep water "full tide" south of fishermans' pontoon. Good to tie up there too and you'll have +2m at LWS) Small island to the west is a good bar-B-Q spot.
Don't tell anyone..
Oh and in the ship you can't have the "specials" on the menu if you eat in the bar, captive audience and they know it..