Well the only way to do a crossover of this two is through coincidence, which involves multiple key events in both series to make a crossover. Like the meanwhile or while this was happening "here" or "there" and thus the crossover turning into whole coincidence of events which leaded to it. Summarized in a Butterfly or Domino Effect which leaded to this events.
The conceptual plot:
Mysterious deaths have been occurring around Japan and each victim in every crime scene have the same pattern, corpse being mutilated to be unrecognizable and most unusual not a single drop of blood in their bodies.
Meanwhile Reinare killed Issei but she in her arrogance didn't make sure he was really dead, so she left him be.
Then by coincidence lovely lady dressed in red with crimson eyes like if hell gazed at one was having walk through the park or better said she smelled the scent of fresh blood that evening, by coincidence she meets the dying boy. Out of pity she ask the boy which was struggling to keep himself conscious if he wished to live, he with all source of strength he could muster he whisper "yes" and she ask one last question are you virgin. To this the boy shows face of misery as if the thoughts crossing his mind were that "I am going to die virgin without doing ecchi things" which suffice as a response for her to bites him on the neck ,thus twisting the life of the boy in a 320 grades degree turning it into un-life.
Instead of rias it would be Seras and the irony is that Issei was Virgin and is of an opposite gender, thus he can be turned into a vampire by Sera.
Since Issei will need to feed, Seras which has already embraced her nature will train him the same way her master did to her with insults and names. Now the problem with this would how would this develop. Since you need to balance the setting so the story may retain the Lightheartedness of DxD and Horrific Violence and Vicious Mutilation of Hellsing.
Issei ends up with the motivation of making a vampire harem since most of the girls of DxD are virgins. And his first life taken would be the sweet and innocent Asia being turned into a vampire which due to the nature of her innocent mind she might be the most vicious due to the transformation pulling out hidden emotions.
Now what can be the bridge or coincidence between the worlds so the Hellsing character passes through the other world? Simple, the death of the god of the Bible in the war, which might have damage to the fabric of space and time in certain way, meanwhile a certain vampire which is here and same time not with his irregular existence he opened said fabric and dragged her servant with him. The reason why Seras is there was because she had lead of her to Alucard whereabouts which leaded to the city/town.
Any who take this idea please take in consideration and of issei as a Kaneki suffering thinking what he has become. As well that he possess a sacred gear which has the soul of dragon thus making him prideful and aggressive when everything isn't his way.
And think of Seras and Alucard as a different kind of Vampire than the ones from DxD. Since the ones from Hellsing devour the souls and every essence of the person they feed on thus consuming the sacred gear thus making the victim a familiar. While those of Dxd only consume blood and turn other people into vampire without much though if they are or not immaculate or are of an opposite gender.
PS: Don't turn Issei into being a reincarnation of Alucard. Everything is just a coincidence of unrelated people meeting all simple coincidence.
A/N: Any interested in this madness taken possibly from one of JoJo's Bizarre Adventure Manga or Baccano please PM and leave a Review with your opinion about.
Another note: I might possibly publish a true story and not challenge. A Crossover between Berserk and Monster Girl series mostly based on Monster Girl Encyclopedia, Monster Girl Quest, Daily Live with Monster Girls, Violated Hero/Okasare Yuusha and others.