From the text for Dabbler in Action 4, there's yet another reason the plan in the OP won't work, even if it did work on defaults from other skills rather than attributes, which is that Dabbling has a cap on skill. It's never better than the 1-CP skill level would be.
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Originally Posted by Action 4
Alone or combined with Jack of All Trades (p. 32), Dabbler cannot improve a skill to the level that one or more points would buy. Maximum default level is one lower than the one point level.
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An all-around Scotty-style starship engineer does need a rather intimidating list of skills by RAW. It's a common enough character trope, though, and probably shouldn't demand that many CP to build the characters for most games. You might want to look into using a Wildcard skill (Engineer!), or just start ruthlessly combining all the design/repair/use skills into fewer variants and branches.