This is an excellent and interesting question; I am only sorry it comes out of a time when you and your husband are struggling with a different situation. Before I answer the technical issue, let me wish for you and your husband that Hashem bring you to a place of peace and happiness soon, whether through these treatments or in some other way, and that you have many happy and fulfilling years together.

 

As for your question, it makes two assumptions, each of which are questionable. First, you assume that the Torah's prohibition against bestiality is a prohibition of mixing the genetic materials of humans and animals, but I am not so sure-- I think the Torah prohibited the act  humans having intercourse with animals, but I am not sure there's a prohibition against combining their genetic material. For that matter, and I don't know why one would want to do it, it's not clear that Jewish law would prohibit in vitro mixing of the genetic material of humans who are not allowed to have relations.

 

Meaning, if a brother and sister were to donate sperm and egg, I think there are reasons it's not allowed, but those reasons aren't the primary incest prohibitions. ( I believe that R. Moshe Feinstein originally opposed inseminating a married woman as adultery, but I think that was where the insemination happened into her literally, not the in vitro fertilization of egg and sperm in the laboratory).

 

This is actually a complex discussion in Jewish law, but here, I don't think bestiality would be an issue. That's especially true because there is no intent to grow the resulting mixture into an embryo, let alone try to have it come to term and be born.  That's a complicated question as well, but fertilizing a human egg with human sperm, but then not letting it proceed past a very early stage of development is also not the same as abortion (it's not necessarily allowed, but it's not abortion).

 

So here, where the sperm and egg are joined only to see if it works, and then the process is stopped, I see two reasons it's not an issue: first, the question of whether joining sperm and egg is thought of as a sexual act that would be prohibited and second, whether joining a sperm and egg with the intent of shortcircuiting the process before it reaches any meaningful development is a problem.

 

Again, best of luck with your path.

In 1995, the Conservative Movement's Committee on Jewish Law and Standards approved Rabbi Aaron Mackler's opinion that Jewish law permits the use IVF. Rabbi Mackler stated, "The use of IVF in such situations accords with our responsibility to be both reverent and active in our partnership with God." At the same time, Rabbi Mackler emphasized that a couple struggling with infertility is under no obligation to undergo a procedure like IVF. Indeed, in a separate paper, Rabbi Elliot Dorff makes clear that "our ability to procreate is not the source of our ultimate, divine worth." A couple may utilize IVF if they desire, but also can and should be clear of conscience, at least from a Jewish and/or theological perspective, if they decide it is not right for them, or if even that procedure does not work.
 
There have been few significant legal objections to IVF even in the Orthodox world, but most objections stem from a concern that the husband might "emit seed in vain," that is to say, he would have to produce semen to be used for the procedure, most of which would ultimately be destroyed and discarded, not used for implantation. The halakhic tradition classically considers "the emission of seed in vain," to be tantamount to a capital offense, like idolatry and murder (Babylonian Talmud, Nidah 13a). This is because the character in the biblical story on which the rule is based, Onan in Genesis 38:6-10, incurs the death penalty. 
 
There are many legal, moral, and theological problems with the legal concept of "the emission of seed in vain." But in the case of IVF, since the husband specifically expels semen in order to conceive, the concept should not apply. Rabbi Mackler makes this clear in his responsum. Rabbi Elliot Dorff makes a similar argument in his 1994 responsum on Artificial Insemination.
 
This argument, I think, holds true even for semen that is emitted for the purposes of testing whether it is viable. The man, after all, produces the semen in this case for a purpose directly related to procreation.
 
That is one part of the answer to the question: whether IVF, and whether this kind of testing, is acceptable at all. Regarding the specific method of the testing, and the possibility that it might constitute bestiality: In his responsum on Artificial Insemination, Rabbi Elliot Dorff examined whether placing another man's sperm into a married woman would constitute adultery. In other words, does adultery require a sexual act? Ultimately, Rabbi Dorff argues that “[Donor Insemination] should not be construed as adultery either theologically, legally, or morally.” Adultery requires actual sexual contact.
 
The same is true for bestiality. In the scenario described, there is no sexual act between a human and an animal. There is simply the experimental mixture of genetic material. Moreover, the husband's intention obviously is not to implant hamster eggs, but rather to ultimately know if his sperm is viable for his wife. Since there is no sexual act occurring, or even a sexual or procreative intention, the procedure should not be considered forbidden in any way.

 

This answer, of course, would be quite different if the intention of the man or of the scientists was actually to create a human-hamster hybrid creature. Without a sexual act, it still may not fall under the category of bestiality, but would certainly be prohibited on other grounds.

Bestiality is defined as sexual intercourse between a person and an animal. The procedure you describe does not involve sexual intercourse of any kind. (It moreover does not, as far as I can tell from my inexpert research into the question, produce viable embryos.)

As you have observed, most, if not all, rabbinic authorities view IVF as a legitimate medical therapy for infertility. IVF is also a physically, emotionally and financially challenging procedure. I pray that if you and your husband choose to attempt it that you find yourself able to proceed free, at least, of further spiritual and ethical doubts. May God bless you with an answer to your prayers.