... players must do almost every sidequest in order to reach 5th Level before Omu ... So you're implying they'll go back to Port Nyanzaru a few times? ... but it may delay the characters a bit...
The party only need go back to Port Nyanzaru three times. I think they head to Fort Beluarian right away and then back to Port Nyanzaru right away -- so that one barely counts. Then, they loop upstream the River Tiryki to the place that River/Flask told them about (Dungrunglung) and have Eku lead them to a peaceful Nangalore (to get it on their map), a peaceful Heart of Ubtao, and then to Mbala and/or Orolunga before downstreaming the River Soshenstar back to Port (stopping at the Order of Gauntlet camps, the goblin village for the amulet, and to Vorn to walk him home). They can then tell the Lords' Alliance member, Lerek Dashlynd about those two locations Eku trekked them to (and Syndra and Wakanga about the teleportatoin circle at the Heart of Ubtao), but lead the sea journey with Captain Ortimay in the Brazen Pegasus to Shilku Bay. Their sailing ship can meet the Brazen Pegasus in Jahaka Bay to fight the pirates. Then they go back to Fort Beluarian before going to Port Nyanzaru. When they arrive, they say their goodbyes before heading to the River Olung areas via the teleportation circle, with Ortimay meeting the party at Mezro in order to hit the Hvalspyd before Nangalore, Kir Sabal, and Omu. I think the two Wrecks are the most-likely marked locations to be skipped, but flying to the Wreck of the Star Goddess on the way to Omu works nicely. The Wreck of the Star Goddess can be seen from Mbala on a check, or the Albino Dwarves of Hrakhamar can put it on the map. Finding the Wreck of the Narwhal probably requires that The Tortle Package addendum be utilized for the Tortle guide, Eeyal. If you do use it, I suggest that you run the Snout of Omgar before Shilku Bay, as it is great material and will probably bump the party up one level (still within the Level 6 range suggested by the time the party enters Omu). If you feel strapped for time, I would throw out Firefinger, all ruins (well, except Omu of course), and all of the Ataaz locations.
The party could do the Rivers Tiryki and Soshenstar in reverse. It doesn't matter, but what does is that they purchase a ride on the Brazen Pegasus, acquire their own sailing ship, and link up the teleportation circle. There are other possibilities, but this general plan allows the party the most coverage of the marked locations on the map before Omu (and give them a two-to three month time to complete the entire module). If they don't want to do it -- that's fine, too. You can lead a horse to water, but you can't make him drink.
There are a few good stories to tell in Port Nyanzaru when the party reaches Level 3 and 4. They will be powerful enough to challenge gladiators and merchant princes, especially with a little help or guidance from allied NPCs. They can buy minor magic shields, minor magic weapons, potions, and spellbooks/scrolls -- or trade their goods (or the construct Vorn with the control amulet) to create a broadly-useful inventory. They can purchase more-expensive beasts (of burden or for flavor). They can watch as Jessamine and Syndra wither away, increasing their desire to move things along quickly. New rumors and new sidequests (or sidequest completion criteria having been met) are extremely-important to this adventure.
If party members die, so be it. I try to get them to Level 3 without too-many hitches (Eku helps here, as do a few marked locations that can't really be engaged in combat early-on) and then they are on their own to make mistakes or take egregious damage from traps (e.g., Camp Righteous), monsters (e.g., the dragon, pirate hordes, frost giants), and the environment (e.g., falling from great heights at Kir Sabal, Firefinger, or on their journey in the air to Omu). If a party member dies, the surrogates can be traded in --
http://dnd.wizards.com/articles/news/tomb-annihilation -- usually at the average level of the party.
If the party gets to Level 6 or 8 easily, then they still have quite a ways to go without facing instant-kill encounters every step of the way until the module's closure. I don't think that much of the jungle dangers or encumbrance will make much of a difference by this point. If early-on you find that a certain character is really overdoing their gear allotment, then just kill the PC off (he or she drowns from a mishap in armor or chokes himself/herself to death on his/her own backpack straps). Then just threaten to do the same the next time a character goes too-far.
For ammo, I find it annoying/hard to keep track of it. There are caches or outposts that probably contain quivers full of ammo of all types even when random encounters and/or marked locations don't. Just keep track of magical, adamantine, and silvered ammo. NPCs, beasts, and food are easy to deal with. As I mentioned -- two or three guides or guide pairs at a time and maybe up to three side questers as well (and maybe two or three beasts, too! Why not?!). NPC guides and questers are mostly-restricted by Loyalty (page 93 of the Dungeon Master's Guide and page 34 of the Tomb of Annihilation), and even if you get a lot of NPCs into a combat or series of combats, there are always the rules on page 250 of the Dungeon Master's Guide on Handling Mobs. The beasts are native the jungle. They can probably help with finding food and water even better than most PCs or NPCs with +7 or +8 Survival.
You would be hard-pressed to complete this module in 6 months if you only meet once a week for a single 4h session. If you want to play once a month, then try the Lost Mine Of Phandelver. I think it would work best if you met once a week up to Omu and then meet twice a week. Tomb of Annihilation is equally as long as Storm King's Thunder, but I think Tomb can be done faster. If you have a disjointed and unorganized group that only meets occasionally, I suggest combining Hoard of the Dragon Queen, Scourge of the Sword Coast, and maybe some of the early parts of Storm King's Thunder -- stringing them together with teleportation circles and the like. The blogs we've linked to in the past few posts generally agree that Tomb of Annihilation is the best among these.