Merely substituting words one for one from one's own language simply will not do. I have read texts in Interlingua which were little more than relexified English, and to be honest they seemed rather strange to me
Yes, my own initial attempts have been quite clumsy in this regard.
...even when the "source" and "target" languages come from the same or similar linguistic families. And a mere list of signs for words will not by itself capture the syntax and "spirit."
Well, that's one of the big challenges isn't it? Machine translation versus free translation? From where I'm sitting I can't see any way to have an international language without a strong bias either toward a preferred set of cultural referents like those of western civilizations OR toward a more bloodless culturally neutral language which many parties consensually adopt and lose all that 'spirit'. For sure I can't imagine a worse language than english. It is nearly incomprehensible at times to me and I've been speaking it all my life. Its one great advantage for americans at least is that people from anywhere can completely mangle it grammatically, with accents, and rhythm and it is still understandable. You can say most things to a cosmopolitan american with twenty words of bad english and hand gestures.
So much comes down to the goal. A language for international diplomacy? An international trade lingua franca? A scientific/technical language for academia? Common language for pen pals? I could see how each of these would have very different constraints and requirements.
Which brings me back to your original phonetic english question. Is your personal goal the promotion of an international language for one or more of these purposes? Or is your personal goal more of a curiosity or academic interest?
For me these considerations are almost entirely edutainment. Except for the purposes of learning interlingua itself I don't think I'll have much use for the international component or penpals.
Now, this has benefitted some others in other 'hobbies' of mine and have on several occasions been profitable financially.
I like contributing, even if the principle goal was self gratification of a curious itch. My brother says my life is lived on a 'need to know' basis in the sense of once I get it in my head, I need to learn it, do it, master it.