I have a particular interest in this as I use it most days. For a cyclist there's no easy solution to the current arrangement other than getting off and walking which kind of defeats the point.
Anyone going North<>South is meant to use the flyover, to a cyclist though it is obviously a hill, fine if you are wanting the exercise, a problem if you don't. It's also fairly windy up there, the traffic is moving pretty fast and you have to filter into the middle lane before you arrive at the flyover.
Alternatively you can take the roundabout underneath. This is fairly easy coming north as the 'straight on' lane bypasses most of the roundabout but then puts you right in the lane where HGVs are constantly entering and exiting the Freeport, not always fun.
Coming south is even worse. As you arrive at the roundabout the lanes kink to the right, at this point even if you have primary position in lane one, the road encourages drivers in lane two to keep going in a directly straight line in to lane one, cutting a cyclist up, pinching them against a kerb and possibly crushing them against the pedestrian barrier, then they turn left right across your path.
As you get on to the roundabout you then have to face all the traffic coming from Princess Way A5036 to your left, described as 'already one of the busiest roads in europe' much of the traffic is once again HGVs heading for the Freeport, the Liverpool Echo recently reported that activity at the port is 'due to expand rapidly', which can only make the situation worse.
The Seaforth Flyover and roundabout present a large obstacle for people wishing to cycle from north Liverpool into the city but I think it can be massively improved with some simple measures which would have an insignificant effect on traffic flow.
Blue is bicycles, green is pedestrians.
South > North is straightforward, a segregated lane can be included in the existing verge.
North > South a segregated path can be built into the pavement/verge to remove the pinch point and allow a protected left turn that will allow for a cycle track to run along the residential streets parallel with the A5036. Then a toucan crossing to get cycles across the front of the joining traffic. On the exit the pedestrian space narrows significantly, but it could be fixed by either shifting the road to the right a few feet, or taking the land from the property adjacent. This looks like a former demolished school so the land may already belong to the authority.
There's is plenty of space for the cycle lane to completely encompass the entire roundabout, although the north/south movement seems to be where most of the cycle traffic is and where the priority lies.