I have the Moulton TSR, but I don't stand to pedal as I can't even stand the bit of bobbing with seated climbing.
The front suspension is adjustable, so it can be optimized somewhat to have less bobbing while giving reasonable compliance for the suspension.
The rear elastomer is not adjustable, but its rather hard, so there is less bobbing from it.
All said, there will be bobbing during climbing unless on easy enough gears.
Easy gears may not be at all possible if riding in a group and trying no be ahead or not getting dropped.
I have only tried the Birdy on a few occasions.
The front and rear elastomers can be changed to very hard ones to almost eliminate bobbing.
However, I found that the bike felt very harsh with such an option and defeats the purpose of using it.