Above means North of the Chickahominy. I always associate above as being north. As you say Johnston had nothing above the Chickahominy which means there were no troops to stop an advance towards Richmond. What I would consider an aggressive move would be for a combined attack by McClellan on the 1st of June (which is what Longstreet expected) both below and above the Chickahominy.
View attachment 372941
By Map by Hal Jespersen,
www.posix.com/CW, CC BY 3.0,
https://commons.wikimedia.org/w/index.php?curid=4494834
Put everybody in. Fix Johnston below the river and cross and envelope above with crossings at Mechanicsville. This is assuming that McClellan had pontoon bridges available. If not, get them from Ft. Monroe and attack after the bridges arrive and are placed. Going by the OP Johnston is still around so this show of force might just scare Johnston enough that he abandons Richmond as was his custom.
Okay, I think I see the misunderstanding here, which is that you're not aware of the problem with attacking Richmond north of the Chickahominy.
Richmond isn't north of the Chickahominy. There's no "towards" there - you're moving parallel to the city, not towards it.
The reason why there's nothing there to defend Richmond north of the Chickahominy is because, well... there isn't a way into Richmond north of the Chickahominy - it has to be an assault crossing of a flooded river (the Chickahominy was flooded on the morning of the 1st - at least one bridge collapsed under Franklin, as in under
general Franklin himself, and dumped him in the river) and most of McClellan's bridging effort for the last week and a half has gone into bridging between Bottom's Bridge and the Upper Trestle Bridge (and indeed most of the effort would continue to go into making sure these bridges were fit for purpose - see the note about Franklin being dropped in a river by the bridge that was supposed to take his corps across).
AP Hill (shown on the map) wasn't involved in the Seven Pines fighting, just as one example of a unit which was available to respond, and an opposed river crossing with pontoon bridges is a really bad idea when your opponent has troops available to respond.
If what you're basically suggesting is having 2nd, 3rd, 4th Corps attacking south of the river to fix Johnston, and then having 5th and 6th Corps making their assault crossing, the problem that immediately comes up is that as of Seven Pines Johnston has about 140 regiments of all arms in the Richmond battlespace exclusive of the Richmond garrison itself. (That's basically the number of companies divided by ten.) Each of McClellan's binary corps has about 27-30 regiments of all arms (as a rough number - 4th Corps for example has about 28-29 regiments of all arms, while 6th Corps has about 27 and 3rd Corps also has about 27.)
The holding attack south of the river (by about 85 regiments of all arms, going against fortifications) can't really be expected to tie up more than a hundred Confederate regiments of all arms - if they did that well they'd be
outperforming - and it still leaves forty regiments of all arms to cover the Chickahominy, which means that 5th and 6th Corps (total about 55 regiments of all arms) are being expected to succeed at roughly 3:2 odds in making an attack over a river, then uphill against forts.
It's not simple at all. In fact I think it's the sort of situation Johnston would be very pleased to be in, because it means the Union troops are battering themselves against his defences in situations guaranteed to cause massive casualties.
Yes, McClellan has some extra troops on top of what are in his corps - but they're not available to attack. In fact this slightly overstates the available attacking strength, because McClellan can't just leave his supply base and rear areas undefended.