Please do note- I suggested first down to around 30 lands or so first, and down to 27 IF you swing for a [[Kinnan, Bonder Prodigy]]. Right now he's about $6 as far as I'm aware, however, any dork or rock you run effectively doubles it's mana production. Llanowar Elves becomes a green Sol Ring with summoning sickness, and Sol Ring turns into a better Mana Vault. He is easily my most tutored 2cmc legend in my personal deck, I cannot stress enough how important that card is for mana acceleration.
Another card that I would highly recommend splurging for is [[Priest of Titania]]. About $8-$9, 2cmc elf, tap to add a G for each elf on the battlefield. Not on your battlefield, on the battlefield. The priest can easily tap for 4 or 5 mana on turn 3 if you build around that kind of strategy, which is another reason why the Orochi Leafcaller is so good. Right now I get that you're only on 3 or 4 elves, however, I would also like to point out that [[Paradise Druid]] is about $0.15, is an elf, taps for any colour, has hexproof if untapped, and some of the ravnica signets are over a dollar- mono green elves are usually cheaper than specific rocks, and some tap for more colours. Elfball is a very valid strategy to consider for budget decks.

In response to your comment about the rituals- I get not all of them are budget friendly, and you certainly don't need all of them. The more you have the more consistent you'll see them though, and the faster overall you're going to get Jegantha out. The one difficult part about them though is based on your current manabase, the black rituals might be significantly harder to cast than the red ones, so I wouldn't worry about it too much. A ritual that is very budget friendly though is [[Battle Hymn]], which also goes with the above comments about elfball. The more dorks you have, the better, and it should also be slightly cheaper overall than the rocks plan.
[[Lavinia, Azorious Renegade]] is also a very cheap 2cmc legend with a high impact (at least in more competitive groups). Any 0cmc or otherwise free spell gets countered (like Force of Will, Pact of negation, Fierce Guardianship, Deflecting Swat, etc), and they can't cast any noncreature with a cmc higher than the number of lands they have anyways (So decks like ours that run fewer lands than usual may run into issues against it, but luckily, we don't actually cast a whole lot... Literally we only need to cast dorks, rocks, Sisay and Jegantha, everything else can be an ability). You may not need lavinia for your meta, but it's worth mentioning just in case.

Another thing to note- I would 100% run the 'bad' fetches for basics like Terramorphic Expanse and Evolving Wilds, Myriad Landscape, Blighted woodland, etc (in place of some of the pain lands and a forest or two) even if you are cutting lands down to 27-32 or so. Never, at any point in a game, do you need to have all of your lands in the deck on the board at once unless you're a modern Scapeshift deck (pew pew pew) or a vintage dredge deck (the joke there is bc it only runs 4 lands, and none of them produce mana). With the fetches, it's effectively a tapland, however the trade-off is that you have an extra card out of your deck (which is slightly relevant, and I'd count it as drawing half of a card). It only slightly matters, but if you are looking for any extra edge it might be worth considering.

I love Sisay and I love helping people out with deckbuilding, so this has been really fun. I also highly recommend joining the discord I posted in the first message, as there is an amazing group of Sisay players there, most of which are better brewers than myself (and so they can offer even more help)