Jaye16 made a large post about this yesterday evening citing dictionaries and Google Ngrams, but now seems to have deleted it. That's ok. It's made me have a few more thoughts on this:
I've decided that both 'by my boat' and 'with my boat' sound bad. Personally, I think 'by my boat' sounds the worst of the two, but that's mainly because of the intervening possessive. 'Travelling by boat' is the most idiomatic usage in English, but since we have to obligatorily get the possessive μου into it, that seems to trigger weird English syntax in translation.
While 'with my boat' seems ok, it seems to me only borderline grammatical in this sense, and probably only feels right because you can use it perfectly normally to say that the boat is on the roof of your car or something like that. Whereas 'by my boat' just seems wrong to me. On its own 'by boat' is a fairly fossilised and idiomatic expression for means of conveyance, and so that's why (at least for me) it doesn't work when there's in inserted possessive.
'on my boat' or 'in my boat' seem to be the best English for me now, with 'with my boat' only begrudgingly accepted. I don't like 'by my boat' at all.
Edit: On reflection I now agree that jaye16 is right that the other uses of Greek με seem to be triggering this 'with my boat' construction over ones that are grammatically more acceptable / more accurate in translation.
Oh, I thought I deleted that in time. Yes, as you explain we do need the "μου" /"my" in that sentence so it would have to be "on my boat". After consultation with the team, however, it was decided that "with" and "in" could also be accepted.
Thanks very much. We try to make every exercise as precise as possible and your input has been both enlightening and supportive.
My default understanding of "I travel with my boat" would be that either, like mentioned above, I have the boat on the roof of the car or something like I own a racing yacht which I can have shipped (either by hiring a crew or sticking it on a semi) to the next regatta, but sometimes I might also travel along with it. I take it this Greek sentence carries both these meanings as well as the straightforward "travelling on"?
Sure, 'by' is more usually used for means of transportation, and 'with' for accompaniment, but as a native speaker of Eng., I'm pretty sure I could say something like "I'm travelling with the ferry (to wherever)." Although that may depend on the exact context of the size of the boat and the scale of the transport, I suppose.