Being the nerd I am, I observed the comings and goings at the main border post between Colombia and Ecuador during the 2 crossings I did with a bike in June this year and it is my opinion that if you know what to do, it's easily possible to do immigration to leave Colombia and avoid visiting customs to check your bike out.
Then do customs and immigration upon entering Ecuador. Or just immigration. This will make things tricky if wanting to get the bike out of Ecuador at any southern border, but might suit you if you want to indefinitely park in Ecuador and fly out.
Myself and 2 other bike travellers I spoke with (we all travelled independently from each other: total combined distance in Colombia maybe 10.000km) were never stopped at any road block/papers check. Actually I lie, one traffic person somewhere north of Bogota tried to flag me down, but I didn't stop as I wouldn't have understood what he wanted from me, so I saved us both the hassle. The army have guns and are looking for "terrorists". The traffic cop: no comment.
Summary: assuming the bike won't enter Colombia again, just ride out after doing immigration.
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