I'll label the summer ones W to E, Northern NH1 Nh2 Nh3 NH4, the lows l1 l2lL3 and l4, and the Southern highs SH1 SH2 Sh3. In winter I'll labe them l1 L2 l3 L4 l5 and h1 H2 h3 H4 h5. Uppercase vs lower case is whether they're a strong or weak system.
Another circulation effect we haven't mentioned is a general shoving of warm water and warming air westward by the easterlies just to the north and south of that intertropical convergence zone - the string of near-equator lows. Google "Walker cell". It's something that
develops across our huge Pacific, and probably would be even stronger above your three-quarters-of-a-world ocean. That generates a low around the east coast of a continent, and a high over trhe affected western coast. In your winter there wouldn't be much of this going on, since the ITCZ winds up totally south of your landmass.
Starting with your general High-Low placement here's what I think would happen.
Summer: l1 weakens or goes away and NH1 and SH1 shift together more. l2 and L3 drift north by five or ten degrees, with l2 swelling into L2. An ITCZ line bends north over land. l4 shifts eastward to become that coastal low of the Walker circulation, swelling into a bigger L4, but southeast of where you show it. A band or trough of low will extent most of the way around the backside of the globe, at maybe just 5 or 10 degrees N. That L4 low is the recipient of a huge amount of warm wet oceanic air all summer, and the coast where you show l4 is probably stormy and soggy. maybe June to November would be a hurricane season in your SE, from maybe 10 degrees N to 40 or so N. Nh2 and Nh3 probably coalesce into a single weak high, call it Nh23. I look at earthly maps and don't see discrete highs so closely spaced as your four northern ones.
A lot of your summer west-coast circulation is going to be N to S along the coast, with that big high pulling slightly cooler northern air down from your arctic. Cooler equals drier, so we can imagine that to be the equivalent of the airflow along the Andes. I assume it's the larger western continent you want dry? Hmmm - your 2/3 ring of mountains and that airflow probably could justify an interior desert. The very north and east edges, outside of the mountains, might be more damp. Air crossing that long inland sea couldn't help but pick up *some* moisture. Based on guesses before you draw in all the airflow, the inside of the tip of the hook of mountains in the southwestern continent/island could be pretty dry.
In winter your l1 L2 and l5 are probably about right. A winter 60-ish degree N string of lows appears to make more of a trough than beads on a string, if you will. I would guess the continental high would almost override l3 and L4 - say, erase both and shove an even bigger H4 up to about 30 degr N, due S of where you show L4. That's kind of what happens with earth's Asia in the winter.
For your winter map you may want to sketch in the slightly south-of-equator trough of lows. The clockwise outflow from northern hemisphere highs will be blowing kind of NE to SW when it gets to the equator Where there are pronounced lows - spots or blobs - it could torque to more NW to SE flow entering them. But you don't have southern landmases to bend the ITCZ much south though, so your winter is going to have close to the ideal ne to sw flow.that south-of-equator trough. Without significant southern landmasses, the airflow will stay more idealized. You'll have a conveyor belt of easterlies whooshing through those southern islands and all the way around the back of the globe, all winter.
What level of technology are your inhabitants? Once they develop long-range ocean travel, say clipper-ship sophistication, it'd be interesting to see how many traders risk a 3/4 circumnavigation to get from your west coast to east coast. That'd be an insane risk for galleys or galleons ;-).