I cannot imagine an initiative system worse than all the players go first, then all of the monsters go (or vice versa).
Challenge Accepted!
(Note: in all the following proposed systems, ties go to the person who has the highest charisma. If they both have the same charisma, then go rock-paper-scissors-lizard-Spock)
1. Re-roll initiative every round! Person who gets the highest roll goes, even if they’ve already gone this round. Things lasting until the end/beginning of next turn, last one minute.
2. Play poker! The person who wins get to go first. Use PC gold/monster treasure for stakes. Compare the hands of the losers to determine the remaining initiative order. For extra-terribleness, combine this method with method number one. DM runs all the monster’s hands.
3. Twilight Trivia Challenge! Ask the group questions about Stephenie Meyer’s quartet of books. The more questions you get right, the higher you go. Have a group of teenage girls answer questions for the monsters.
4. Play Hearts! Go in the order of fewest tricks taken to most. If someone successfully shoots the moon, eject them from the game.
5. Random initiative Table!
Roll d% and look-up the result on this table:
[table="width: 200, align: left, class: grid"]
[tr][td]d%[/td] [td]Initiative Order[/td][/tr]
[tr][td]1[/td] [td]90[/td][/tr]
[tr][td]2[/td] [td]51[/td][/tr]
[tr][td]3[/td] [td]67[/td][/tr]
[tr][td]4[/td] [td]Spend combat on another plain of existence. (DM's choice.)[/td][/tr]
[tr][td]5[/td] [td]40[/td][/tr]
[tr][td]6[/td] [td]25[/td][/tr]
[tr][td]7[/td] [td]81[/td][/tr]
[tr][td]8[/td] [td]32[/td][/tr]
[tr][td]9[/td] [td]24[/td][/tr]
[tr][td]10[/td] [td]-∞[/td][/tr]
[tr][td]11[/td] [td]29[/td][/tr]
[tr][td]12[/td] [td]71[/td][/tr]
[tr][td]13[/td] [td]23[/td][/tr]
[tr][td]14[/td] [td]87[/td][/tr]
[tr][td]15[/td] [td]37[/td][/tr]
[tr][td]16[/td] [td]56[/td][/tr]
[tr][td]17[/td] [td]12[/td][/tr]
[tr][td]18[/td] [td]3[/td][/tr]
[tr][td]19[/td] [td]13[/td][/tr]
[tr][td]20[/td] [td]86[/td][/tr]
[tr][td]21[/td] [td]64[/td][/tr]
[tr][td]22[/td] [td]18[/td][/tr]
[tr][td]23[/td] [td]57[/td][/tr]
[tr][td]24[/td] [td]Take a pot shot at the character of your choice before combat.[/td][/tr]
[tr][td]25[/td] [td]91 and you start combat off the battlemat.[/td][/tr]
[tr][td]26[/td] [td]15[/td][/tr]
[tr][td]27[/td] [td]63[/td][/tr]
[tr][td]28[/td] [td]5[/td][/tr]
[tr][td]29[/td] [td]7[/td][/tr]
[tr][td]30[/td] [td]49[/td][/tr]
[tr][td]31[/td] [td]2[/td][/tr]
[tr][td]32[/td] [td]11[/td][/tr]
[tr][td]33[/td] [td]48[/td][/tr]
[tr][td]34[/td] [td]16[/td][/tr]
[tr][td]35[/td] [td]47[/td][/tr]
[tr][td]36[/td] [td]21[/td][/tr]
[tr][td]37[/td] [td]39[/td][/tr]
[tr][td]38[/td] [td]85[/td][/tr]
[tr][td]39[/td] [td]∞[/td][/tr]
[tr][td]40[/td] [td]77[/td][/tr]
[tr][td]41[/td] [td]38[/td][/tr]
[tr][td]42[/td] [td]60[/td][/tr]
[tr][td]43[/td] [td]31[/td][/tr]
[tr][td]44[/td] [td]28[/td][/tr]
[tr][td]45[/td] [td]52[/td][/tr]
[tr][td]46[/td] [td]10[/td][/tr]
[tr][td]47[/td] [td]20[/td][/tr]
[tr][td]48[/td] [td]88[/td][/tr]
[tr][td]49[/td] [td]35[/td][/tr]
[tr][td]50[/td] [td]You go last.[/td][/tr]
[tr][td]51[/td] [td]6[/td][/tr]
[tr][td]52[/td] [td]72[/td][/tr]
[tr][td]53[/td] [td]46[/td][/tr]
[tr][td]54[/td] [td]45[/td][/tr]
[tr][td]55[/td] [td]17[/td][/tr]
[tr][td]56[/td] [td]36[/td][/tr]
[tr][td]57[/td] [td]66[/td][/tr]
[tr][td]58[/td] [td]9[/td][/tr]
[tr][td]59[/td] [td]84[/td][/tr]
[tr][td]60[/td] [td]22[/td][/tr]
[tr][td]61[/td] [td]59[/td][/tr]
[tr][td]62[/td] [td]4[/td][/tr]
[tr][td]63[/td] [td]82[/td][/tr]
[tr][td]64[/td] [td]68[/td][/tr]
[tr][td]65[/td] [td]79[/td][/tr]
[tr][td]66[/td] [td]30[/td][/tr]
[tr][td]67[/td] [td]74[/td][/tr]
[tr][td]68[/td] [td]70[/td][/tr]
[tr][td]69[/td] [td]27[/td][/tr]
[tr][td]70[/td] [td]You go first.[/td][/tr]
[tr][td]71[/td] [td]76[/td][/tr]
[tr][td]72[/td] [td]58[/td][/tr]
[tr][td]73[/td] [td]43[/td][/tr]
[tr][td]74[/td] [td]62[/td][/tr]
[tr][td]75[/td] [td]54[/td][/tr]
[tr][td]76[/td] [td]55[/td][/tr]
[tr][td]77[/td] [td]34[/td][/tr]
[tr][td]78[/td] [td]Turn into a potted plant, you have a shamble speed of 10 feet.[/td][/tr]
[tr][td]79[/td] [td]44[/td][/tr]
[tr][td]80[/td] [td]83[/td][/tr]
[tr][td]91[/td] [td]33[/td][/tr]
[tr][td]82[/td] [td]14[/td][/tr]
[tr][td]83[/td] [td]73[/td][/tr]
[tr][td]84[/td] [td]61[/td][/tr]
[tr][td]85[/td] [td]8[/td][/tr]
[tr][td]86[/td] [td]78[/td][/tr]
[tr][td]87[/td] [td]41[/td][/tr]
[tr][td]88[/td] [td]53[/td][/tr]
[tr][td]89[/td] [td]75[/td][/tr]
[tr][td]90[/td] [td]Drop to 0 hp, initiative is -∞ + 1[/td][/tr]
[tr][td]91[/td] [td]65[/td][/tr]
[tr][td]92[/td] [td]50[/td][/tr]
[tr][td]93[/td] [td]19[/td][/tr]
[tr][td]94[/td] [td]69[/td][/tr]
[tr][td]95[/td] [td]26[/td][/tr]
[tr][td]96[/td] [td]89[/td][/tr]
[tr][td]97[/td] [td]Heal all HP, initiative is ∞ + 1[/td][/tr]
[tr][td]98[/td] [td]42[/td][/tr]
[tr][td]99[/td] [td]1[/td][/tr]
[tr][td]100[/td] [td]80[/td][/tr]
[/table]
Hope this helps!