The strategy that ended up working for me was one where you place Tall-Nuts and Split Peas in the first and second row, as shown below.
Once you have this critical infrastructure set up, the rest of the map is pretty much cakewalk. Just be wary of the walking zombies at the start of a wave - that's what the Pumpkins are for.
- Start your first column of Sunflowers in the third column
- Once you place the last Sunflower in the third, start a fourth column with the Pot Plant, and start adding Sunflowers here as well.
- By the second or third Sunflower in the fourth column, the first Pogo Zombie should spawn.
- Save up and place a Tall-Nut, then a Split Pea in the first and second column of the respective row
- Continue placing Pot Plants and Sunflowers as the Pogo Zombie noms away and gets whittled down by the Snow Pea.
- When the second Pogo Zombie spawns, place the Tall-Nut and the Split Pea again in the first and second column.
- The Tall Nut may still be recharging as the zombie reaches your plants, but it should be done by the time it reaches the first column
- By now you should have almost completed the second row of Sunflowers
- Continue steps 4 & 5 as Pogo Zombies spawn in different rows. Start placing Pots and Split Peas in column 5.
- Note that I used Corn Cobs here instead of Split Peas but I don't think they will be needed - however it's useful to have an extra plant that costs 100 sun around just in case.
- A new wave should happen at some point. The front of your Split Peas (or the corn cobs if you're following to the letter) in Column 5 should be enough to fend off the walking zombies. If not, start placing Split Peas in column 9 (the last column) as they walk past - the backwards shot will take them out.
- Line column 9 with Pumpkins for the rest of the current wave, in time for the next one to start.
- You've won at this stage. Plant Split Peas everywhere not currently taken, Monitor your Tall Nuts, replace them if they get too damaged, and await sweet sweet victory.
P.S. I put down some Corn Cobs but I don't think they are worth it. The Split Peas' slow planting recharge might mean you need an extra plant to take out the walking zombies, so bring the Cobs or something else along just in case. Or, use explosives and just focus on Split-Peas.
P.P.S. I used Double Sunflowers but again, I don't think they're needed. The Tall-Nut and Split Pea have fairly slow recharge timers anyway so you will be waiting on them instead of starving for sun.
P.P.P.S. The Explosives are nice to have in case the Tall-Nut isn't recharged in time (it's only 25 more sun than a Tall-Nut), but I didn't need them at all.