Man, I feel your pain. I've tried to build a deck like this before too. It's not easy.
Neheb, the Eternal always seems like the best choice for big red because when it works, it really works, but I completely agree with you that the deck struggles without him.
Neheb, Dreadhorde Champion has potential. He's not as good as old Neheb at making mana, but finds a decent
balance between ramp and card draw / filtering.
An alternative strategy could be
Krenko, Mob Boss. Make a butt load of tokens then grind them up for mana with things like
Skirk Prospector and
Ashnod's Altar.
Similarly,
Grand Warlord Radha might be worth a consideration. A similar strategy to Krenko,
flood the board with tokens, and use Radha's ability to generate a lot of mana. This has the added benefit of also allowing green, which naturally provides a whole load of great ramp options. And
Savage Ventmaw, who is Radha's best friend.
Gruul has a few options, but I personally think
Grand Warlord Radha might be the best. You also have
Nikya of the Old Ways, but your list isn't super creature heavy so would need a way to kill Nikya to take full advantage (
Ashnod's altar is a great option as it also provides mana. I'll find any excuse I can to recommend that card. It's amazing).
In terms of individual cards, I can think of a couple that might be worth considering:
Mana GeyserBrass's BountyThey can be a little temperamental and quite fickle, but have the potential to be huge.
Mana Geyser has the potential to be huge early on. Usually turn 4 or 5, opponents tend to be tapped out as they've spent their first few turns setting up, so out of nowhere you can get 10+ mana on turn 4 or 5.
Brass's bounty can be seen like a bit of an investment. I think of it like a
battery. You cast it (
charge the
battery) and you can then drain it as you see fit, either all at once for some big spells or in small increments as you do other things. Terrible if you face a lot of mass artifact destruction though.
A really alternative strategy if your focus is big fatties rather than big
X spells could be things like
Jhoira of the Ghitu (or even
Jodah, Archmage Eternal, but then you're in 5 colour and that's a different ball game altogether). Cheat them out rather than pay for them legit with mega ramp. There's a half decent package of cards that let you speed up suspended cards to get them out even quicker.
Hope this helps or gives you food for thought. It might be that none of this sticks closely enough to your original idea or just doesn't appeal to you, which is cool. Let us know what you decide though. I for one would be interested to hear what you came up with.