I suspect that space and matter arise from the same fundamental constituents----that is, geomety and matter are emergent, and have the same underlying dynamics and degrees of freedom.
in that case the properties of matter are intrinsic in any volume of space-----the constants you mention are built into space itself.
in that case matter cannot carry its properties or constants with it and travel thru a tunnel to some domain with different matter. the bridge would have to be made of space, and whose constants would the space have?
In some exotic inflation scenarios there are "domain walls" dividing domains with different physics (different constants, laws perhaps) which travel at the speed of light and which are LETHAL. If a domain wall passes thru your galaxy, you've had it. AFAIK such exotic inflation scenarios do not have much justification and are mostly just piquant fantasy.
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The above is just my own take on it, you asked a speculative question. but the basic problem is that no one so far has offered any scientific justification for assuming that a "multiverse" exists. That is, there is no scientific reason to think that the universe consists of domains with different laws or different physical constants.
People toy with the idea if it appeals to their imaginations. But do you know any justification for it? If so, please tell us!