If you want a longer open time for hide glue use a lower gram strength glue or add an anti-gelling additive. The higher the gram strength the shorter the open time.
Some usable anti-gelling additives are urea, sodium chloride(salt), magnesium chloride(Ice melt) or an acid( acetic(distilled white vinegar), hydrochloric, nitric, phosphoric). There are others which you probably don't want to handle or are difficult to obtain.
I have dissolved glue with distilled white vinegar instead of water and then added water to get the consistency I wanted. No matter what you do heat in needed. If I want to extend open time more I'll add salt or urea but never more that about 15% by weight of glue.
I think the difference between OBG and Titebond liquid is Titebond has so much anti-gel and preservatives that does not gel like HHG and OBG and is not as good for rubbed joints.
High quality hide glue does not stink unless it's gone bad.
I always use distilled water because treated water chemicals tend to darken hide glue.