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Fergus; some thoughts on Bachelor Chess.
	I  went to bed swearing I would not get involved in this, but I woke up
thinking about geometry and Bachelor Chess. I believe the geometry of the
board is a key factor in any game, the first factor to make or break a
game. So, I set up and played your first variant a bit. First, I assumed
the board is a checkerboard, with a white square on the white player's
right corner, so I covered the original 'A' file and set the pieces up.
Both white bishops are on white squares, both black bishops on black; an
interesting asymmetry. The white king starts on a black square; and the
black, on a white, as are their castling squares. Here are two openings I
played:
1)	d4		d5
2)	f1-e3		e6 rather than c6, allowing check
3)	e1-b4		f1-d2 white attempts trade of B for N, black   
declines, but N placement blocks Bs
4)	b3		b7
5)	c4		c5
6)	Pxc5		Pxc5
7)	b4-a5 check	e7-b6 if 7) ... d8-e7, 8) PxP PxP 9) NxP check
8)	BxN check	PxB
9)	PxP		PxP
10)	NxP		a8-a6
white may continue by castling or by c1-g5 check, with much the better
game
The way this played out, I felt black should not directly contest the
center of the board with 1) ... d5
The second opening:
1)	d4		e3 
2)	c1-f4		b8-c6
3)	c3		d5
4)	b1-d2		b6
5)	e4		c8-b7
6)	PxP		PxP
7)	f1-e3		c6-e7
8)	BxP check	KxB probably a serious blunder on white's part
9)	c3-c4		a8-d8
10)	PxP		NxP possibly better if ... BxP
11)	NxN check	BxN
12)	O-O check	e8-c6 white has a passed pawn that is going nowhere fast for
a lost bishop

As I am not the best of players, and cannot play chess against myself,
these openings are not of the highest quality - the B sacrifice, in
particular, was poor, as it could not be followed up. White may actually
have an edge in this variant, but I am certainly not good enough to 
tell, only to suspect this is the case.
However, I do get some clearer impressions of this variant. I think the geometry
is important, as I feel these games are not as subtle as FIDE chess. Two
of six non-royal pieces can never directly interact*, yet they attack the
two most likely squares the opponent's king will occupy. Checks appear to
be easier in the opening. I always had the urge to trade one of my bishops
for the 'opponent's' knight, believing this is advantageous. I think
the openings and patterns of threats are considerably reduced, and less
subtle, because of the geometry. The game gives me more the feel of a
bludgeon than a rapier. This could be because of my style of play,
however. I do believe the knight is worth more than the bishop, and I'd
definitely prefer to have 2 knights and 1 bishop against 2 bishops and 1
knight. I would also think this admittedly very preliminary analysis has some
relevance for your other 7x8 variants and the 58 square variants, 
as the geometry is basically similar. I would suggest a variant of this
game on a 7x9 board, but I wonder if the draw potential goes up. For what
my opinion is worth, I think this is an interesting variant, but FIDE
chess is better, and better because of its' geometry. The 8x8 board
allows better pawn moves in the opening and balances the bishops.
*This would seem to increase the subtlety on the surface, but that's not
the impression I got moving pieces.
I see Peter Aronson** and Doug Chatham anticipated a couple of my observations. 
To Doug, I believe the answer to your question is: 'yes'.
To Peter, I'm real new at this, could you direct me to your sources? Thanks. 
**My error on confusing Spinster queens and Sinister queens - 
apparently Mr. Aronson does not confirm my suspicion that white has 
the advantage in the 7x8 variants, as Sinister Queens is 8x8.