As far as revising this deck is concerned, it might make more sense for me to swap out the 1 copy of Lady for 1 copy of Lillie, but I value hard searching a lot more than draw power post rotation because of the things you mentioned.
Cynthia & Sightseer are a lot weaker than Sycamore & N, and our other draw supporters are even weaker/more situational than that. Sophocles is a decent supporter, but the discard 2 is actually very heavy. In a lot of ways, I think that TV Reporter is actually better than Sophocles by a lot. You still net a total +2 to hand size overall with both supporters, but TV Reporter allowing you to discard after the draw not before the draw gives you more flexibility to discard something you don't feel bad about. I almost never like what I have to discard for Sophocles, and if you're staring at a 4-5 card hand, killing 2 of those cards is usually a really hard decision. Sure, TV Reporter only digs 3 cards deep and not 4, but it's also a lot more universally playable due to the lower discard cost. I wouldn't be surprised if we saw ourselves in a format with 4 Cynthia 4 Sightseer 3-4 TV Reporter in most decks.
I am a HUGE advocate of a 2/2 Zoroark GX line in every deck that has the bench space to use it (this deck isn't one of them). Making Zoroark GX a 4/4 line in a deck and adding a 2/2 back up attacker has potential to be one of the best decks possible just because of the fact that Zoroark GX's Trade got stronger with the "nerf" to draw supporters. Having 3 Zoroark GX's on the bench allows you to dig 6 cards deep into your deck every turn, and that level of potency allows you to open up your supporters for things like Fan Club to get set up and then even Olivia to just guarantee 2 Zoroark GX immediately afterward, but I digress.
The real point I'm after is that I would rather spec my deck lists towards cards that I think have the most value. More draw supporters would be nice, but I don't think Kukui's draw 2 is ever going to save me, and Tate & Liza is just a worse Cynthia that I have a hard time justifying space for in the deck. My problem with Tate & Liza isn't the fact that it leaves you with a 5 card hand size. It's the fact that shuffle draw 5 makes it a lot more difficult for you to actually dig more cards out of your deck. When you have a dead hand of unplayable cards that's 5 or more cards, playing Tate & Liza doesn't thin your deck at all. It rerolls your hand, but it doesn't progress the state of your deck. And if you're sitting on 6+ cards in hand that you can't really play, then Tate & Liza will actually make your deck thicker as a result. Shuffle draw 6 from Cynthia is just a value where you can consistently hand fix while drawing 2 to 3 cards deeper into your deck where Tate & Liza would only draw 1 or 2 cards. I find it hard to justify running a supporter that would only usually draw me 1 to 2 cards deeper into my deck when I could just increase the counts of the cards I need by 1 to 2 instead. Increased counts of important cards both increases the likelihood of seeing them when I do play Cynthia/Sightseer as well as gives my deck more total resources to work with.
I guess the tl;dr version of what I'm trying to say is that I'm trying to optimize my odds of hitting crucial cards after playing draw supporters as opposed to trying to making sure I have a draw supporter in hand at all times. And as previously mentioned, I see this deck as a deck that sets up an engine and then runs it. It doesn't need very many cards in hand after a successful set up, and I actually do think a 4th copy of Guzma is a better decision overall to give the deck more control over its target and its own positioning. To that end, I think I will -1 Tapu Lele GX for +1 Guzma in this list, as well as -1 Lady for +1 Nest Ball to compensate for the small hit in set up consistency. You just really can't afford to get stuck with the wrong active in this deck, ever. As for Lady, you usually won't be swinging for big numbers until turn 2 or 3 anyway, which should be enough time to find the 1 Metal you need. You just never have room on the bench to play 2 Lele either, so if you Lele for Pokemon Fan Club (which you probably will), then that 1 copy of Lady is pretty much lost in the deck anyway. I'll stick to the rule of thumb of "always play 1 more copy of Lele than you expect to actually use in a single game."
If we were talking Rayquaza GX that always wants to have energy in hand to keep attaching and snowballing, then I'd totally agree with 10-12 draw supporters. But not in a deck like UNGX. The only thing UNGX needs to worry about is replacing KO'd Pokemon after it's set up.
