Looks like grapple ships are in? Time to design a ship with no engine and just weapons, and have someone drag me!
I remember when we tried to accomplish this using girders and turrets. It was glorious. I think we even had a design that worked when friendly fire was off?
We did! It worked fucking gloriously... Now there's tools for it though, tether lines are a direct use, and Bumpers will nullify impacts except from specific ramming ships. So you can drag via tethers, and push via bumpers.
Worth noting that EVERY item in the game can be pulled. All stage items, and the motherships, have weight and speed. Motherships can be pulled along, and a single good ship can overcome their engines. However as soon as you break the line, they go pretty quickly back to their wander patterns. Most items slow down very quickly as well, so dragging something towards an enemy and letting it coast in to collision isn't very possible. I haven't tried any push motors for mothership ramming, but even pulling is very tricky. The real worry is that you need to get your centers of mass and thrust just right, and for all practical purposes you need two tethers, set as far apart as you can manage. Luckily they default to the maximum extension when fired, even if you landed the tether very close, it's still very slack, so just leaving it at the same tension will let you haul it evenly.
That said, I've made progress hauling the semi-circular stage pieces, as well as the "long shard" brick looking ones. The biggest thing to worry about is sheer weight. If you get going off-course, the big pieces can glide quite far on inertia. Aiming them becomes a whole new challenge.
I'm imagining a true hauling setup would have two ships. Tether at the rear, as many engines as possible, and bumpers on both SIDES. You tether each ship to a side of the object, thrust forward, and let the bumpers rest against the object, effectively cradling it between two ships. The two pilots would likely have turbojet thrusters for max force, as well as some additional afterburners (the little ones, not the 3-use) so that they could selectively put bursts of thrust to steer the thing, just a little, by having one pilot provide extra thrust while the other keeps normal.
Tether lines also snap if you leave them slack and thrust hard. It's best to pull them taunt, then go full thrust.