If you are completely self sufficient in milk, you should be able to obtain the 4th stomach of the baby animal that is produced as a by product of the milk ;-) Honestly, that would be my approach. I've never heard of gallino rennet, so it's really hard to say. Here is everything (I think) I know about rennet:
Calf/kid/lamb rennet is an enzyme called chymosyn. Enzymes are chemicals that break apart chains of other chemicals (they are catalysts that hydrolise the bond at the connection point). It's important to understand that proteins/fats/carbohydrates are long chains of a few types of atoms, but that the configuration of those atoms changes all along the length of the chains (and branches in the chains). Each configuration has a different shape and gives the chain different chemical properties. Enzymes only break the chains at certain points. Different enzymes break the chains at different points. This leaves different shapes of the pieces that are left -- again with different chemical properties.
Rennet based cheeses are made with a protein called casein. The casein is all wrapped up together in a ball called a "micelle". The micelles are covered with a specific shape of casein protein called "kappa casein". There are 3 different types of casein protein: alpha casein, beta casein and kappa casein. The alpha and beta types are all wrapped up in the center of the micelle and the kappa casein forms hair like structures on the outside of the ball.
Chymosin (and any other enzymatic rennet) cuts the kappa casein. Where it cuts is important. Before the kappa casein is cut, the micelle has an overall positive charge. After the kappa casein is cut, the micelle has an overall negative charge. Once it has an overall negative charge, it can interact with positively charged calcium ions in the milk. The calcium acts like a glue that helps the micelles stick together. This forms a mesh that we call "curds".
The enzymes don't really stop after you add them and they keep cutting the protein down into pieces. Different enzymes produce different shapes of pieces. Each one of these pieces has a different flavour and aroma.
Chymosin is ideal for cheese. It cuts the kappa casein in a very good place so that it will react well with calcium. It also breaks down the protein into pieces that has a nice flavour as the cheese ages. Other enzymes may or may not fare so well.
I have it on good authority that Cardoon thistle produces a good curd and ages well without bitterness. One of the very respected posters here commercially produces a cheese with Cardoon thistle *with cow's milk* and he says that it works really well. He buys actual thistle, though, and wasn't very complimentary of the "thistle rennet" you can buy online. I have also heard reports from other people that it works well.
Some other vegetable rennets have reports of being very bitter. For example, I've read a paper on using papaya skin as rennet and apparently it gets bitter within hours. It's popular in some south east Asian countries for making a milk pudding, but you have to eat it fresh. I have also heard reports that Cardoon thistle produces a bitter cheese, but only with cow's milk :-) So sometimes these reports are completely wrong. :-)
Historically the Romans and Greeks made cheese from fig sap and I'm hoping to give it a try this spring/summer when the sap is actually running :-) There are lots of fig trees where I live. One ancient report (from like 2000 years ago) says that kid rennet produces superior cheese, so who knows :-)
My advice is if you have access to chicken gizzards that you might as well give it a try. It might work well. I might not produce off flavours in the cheese. However, I think it probably makes more sense to use calf/kid/lamb stomach. I appreciate that this is often difficult due to the regulations in how you are allowed to slaughter large animals in many places.
