EDIT: we did it boys, route 2 and 3 implemented
I for one am someone that loves the design of the new Woodie, and I agree with the devs initial conservative strategy of releasing something that is not busted at first, to test the waters.
From game design, it's usually better to start off more nerfed than start out straight overpowered, since the community reacts better to "meh" than to "unfair". Bonus that you can always go up from there, baby steps, and it creates the dopamine hype induced rush of the community when each patch hits.
The issues Woodie have by now are echoed across the community: the issues are in the numbers, not in the design of the forms themselves.
Right now Woodie is just a Wilson that chops fast, because the were forms are rarely useful and situational. People understandably focus on the forms, since it's a new update, but his forms now are "on the side" similar to how willow's Bernie is not necessary to be used. It's different than Wendy, who needs Abigail to function. (Also, please rework Wilson to have some revive mechanics, like in the forge)
The problem with Woodie is a perception and expectation problem.
A lot of hype was built into Woodie, he's a much loved boi by a passionate few, and people had expectations from his very powerful Don't Starve classic version, which does all the chopping and fighting you need, with no downsides, and tons of healing, and weather immunity. In my view his DS form doesn't really fit in the DST lineup, due to its sheer strength at literally everything. In DST, characters should be specialized, and if you want to be ok at everything, you have to be a master of none.
With that said, I offer a few routes of tackling the mechanic balance:
1) Route 1: Remove hunger penalty.
Simple enough, I was surprised to see the hunger being negated. It wasn't even mentioned in the patch notes. I don't even know if that's intended? It seems to use same hunger bar for werebeaver, maybe a coding problem, I've seen worse. If that's the case, don't fire the guy, these things happen. But hunger in DST is the key resource that basically represents time, and this is the first mechanic (apart from rot) that seems to completely negate the slow drain of the hourglass. I think it's bad design to have to do intermittent fasting with woodie and keep him at 10-30 hunger at all times just so you don't loose huge chunks of your internal belly. This is my preferred method, and the community might agree with this change.
2) Route 2: Duration increase twofold, or even 3-fold (for some)
The other way if we want to keep the penalty that steep, is to bump up the bang for your buck. The forms themselves have quite the perks, and the duration increase would be the best for the goose. I would suggest doubling goose time (since it's so good to be fast, and time is money), and triple the duration of Moose and Beaver. This would feel good for the community, I think.
3) Route 3: Halve the penalties of the totems (from -20 sanity and -30 health, to -10 sanity, -15 health)
This might not satisfy the community, but I do agree the health cost of the totems is quite steep, especially if you want to spam the forms. 30 health is a lot. 15 health is two butterflies.
4) Route 4: Remove the health and/or sanity cost of the totems.
Another, (stronger) buff would be to remove the 30 health cost, and even the 20 sanity cost of the idols themselves. I don't prefer this method, since I think the health cost is an important offset balance of Woodie. This would put Woodie in a strong position, since his forms will be very spammable. I would probably keep the sanity cost, and he will become similar to Wortox, always having to be insane to use his perks, but I find that playstyle boring after a while. Some people would like it, some would not. Can you double hit shadow creatures? Depends a bit on that.
5) Route 5: More designs!
This is the more hard work route, which means tweaking and changing the mechanics and designs of the woodie forms in interesting ways in Klei fashion.
Some ideas include:
- allowing transformations to use wormholes,
- making moose charge like Wilbur from shipwrecked instead of right click, by running a few meters than he starts in his fast form stampede,
- making goose form be able to fly over water and over cave voids (but implement a method to save your items if you change outside)
- making werebeaver form actually recharge if you chop enough wood (so you can stay indefinitely, like before)
- making moose be able to one-hit rocks/trees, so that you can gather while killing spiders
- making moose charge deal 2x damage compared to fists (to match the DPS a bit)
- increasing goose speed by a bit (+20% more?)
- making goose be a taunter (like in the forge, when woodie axed the boar), so that goose woodie can become a boss runner
- give goose an attack, with some perks (taunting?)
- make goose have dodge value (if above taunting sounds good)
Other ideas, feel free to suggest on the design part.
These miscellaneous design changes can be mixed with routes 1 through 4, depending on time and need.
Overall, we as the entitled community have a lot of expectations built up, and I feel sorry for Klei, and I know how good they are as game devs and designers, just look where we are.
Art-wise, this project took a crap ton of effort to make, compared to other things we have in DST, and I am sure the devs are disappointed a bit by the reaction.
But know this: The design, coded and art parts are great. It's not you devs it's us. 
The vocal minority on the forums cares about the mechanics and whether their favorite character can do cool and powerful stuff, which is normal, we're passionate about the game.
Cheers