Is a second preimage attack on MD5 feasible?
As far as I am aware, there are no practical known second pre-image attacks on MD5, under the conditions you listed.

However: if the attacker can control any part of the original, I would worry about using MD5 in this setting.  Its security in this setting may be fragile and there may well be cleverer attacks than anything currently in the literature.  I wouldn't be shocked to discover that second pre-image attacks are possible if the attacker has control over part of the original, even if we assume that the original starts with some unpredictable stuff before the part that the adversary can control.

So using MD5 in this way in new systems would not be prudent.  (I don't think I'm telling you anything you don't already know...)