Would it not make more sense that second teams play the same side the first team is playing, in X league and above, to get more competitive matches and play different opposition.
I can only speak on behalf of Moortown, but our seconds started in the 'premier league' playing 7 matches, of which 5 of them were away, as the bigger clubs wouldn't travel. We then asked to move to the league below and played 8 games of which 3 have been against Keighley and we are playing Old Brods again this Saturday which will be the 3rd time of playing them in the 9 games.
If Moortown 1st team are playing Scarbrough away then take both 1st and 2nds up to play and make a day out of it, then vica vera on the return fixture, this giving more varied games for the 2nd teams but then also wouldn't effect the leagues below by entering second teams into Yorkshire 3/4 etc.