One option is to "delta hedge" by adding a totally separate setup in a different expiration to take on the job of defending the call wing from further upside. In this case, I could consider adding long delta (since my net delta is short) using a short put vertical (which is a delta positive setup) in an expiry some time in August.
However, I want to be careful doing too much of this. First, adding a separate setup increases risk. For example, if price whipsaws back to the downside, I could very well find myself having to defend two put sides, whereas now I would only have to potentially defend the one pictured here. Secondly, should we get a down move, the long delta portion of the setup would increase incrementally, since I would now have on one more long delta unit than I have short delta units, and I could find myself scrambling to balance overly long delta in the setup, essentially chasing my tail in an anally retentive effort to keep the setup delta neutral.
For these reasons, I do any delta hedging I feel I have to do small and sparingly and only in circumstances where I can't comfortably or profitably roll a defensive side. Additionally, I set up a delta hedge as though it were an "original setup"; I don't try to move it in closer to current price to get more credit out of it to make up for the losses experienced by the side I'm defending, since again I want to lessen the possibility that my delta hedge will become an entirely separate headache if price decides to whipsaw back into it. Thirdly, I generally take it off as soon as it's served its purpose and I can do so profitably (e.g., the side I'm defending is reaching expiry, and I'm on the verge of rolling it anyways). In some circumstances, "profitably" for a delta hedge can be basically anything more than scratch ... .