Va'eira- Does the timeline work?

For this week's post, I'd like to take a couple of different explanations regarding the course of the plagues that were brought on the Egyptians and see if these explanations actually piece together to work on a proposed overall timeline for the course of the plagues.

Regarding the plague of blood that was brought on the Egyptians:

"The seven-day period was filled after Hashem struck the river." ~Shemot 7:25

Rashi on this verse and Shemot Rabbah 9:12 explain that each plague spanned an entire month of time. This time incorporates both the time during which the Egyptians were plagued with each curse and the time during which they were warned or Pharoah was given time to change his ways. One interpretation explains that there was 1 week of plague and 3 weeks of warning/repentance time, while another interpretation says that there were 3 weeks of plague and 1 week of warning/repentance time. Either way, the full timespan for each plague was 1 month.

Regarding the plague of lice that was brought on the Egyptians:

"So they did: Aaron stretched out his hand with his staff and struck the dust of the land, and the lice-infestation was on man and beast; all the dust of the land became lice, throughout the land of Egypt." ~Shemot 8:13

The Midrash Says on the book of Shemot explains that once the plague of lice was inflicted on the Egyptians, their was no useable ground left for the Israelites to perform any of the slave labor that they had been forced to do in the past. They could not make bricks, because the land was unusable; they could not be made to sweep the streets, because the dust had all become lice. The Torah Anthology Me'Am Lo'ez Book 4 and The Midrash Says on this passage explain that even if someone dug 1 Amah (~24 inches) down into the ground, they still would only find lice- there was no dirt to be found at all. 

As The Midrash Says continues on through the plague of Wild Beasts, it explains that the Egyptians tried to make the Israelites continue working by making them carry their children far distances, but the beasts would come and take the children from the hands of the Israelites. In this way, the Israelites escaped another attempted form of labor.

In Ein Yaakov: The Ethical and Inspirational Teachings of the Talmud, compiled by R' Yaakov Ibn Chaviv, it explains that the Jews were redeemed from their hard work  6 months before their exodus from Egypt. 

Based on what we learn above, that 

• each plague spanned (in some form) an entire month
• the Israelites were unable to be forced into slave labor after the plague of lice ruined all of the dirt in Egypt
• the Israelites were unable to be forced into slave labor for the 6 months preceding their exodus

does this timeline fit together?

Let's establish a timeline that lines up with the series of plagues:

Month 1: Blood

Month 2: Frogs

Month 3: Lice **

Month 4: Wild Beasts 

Month 5: Pestilence

Month 6: Boils

Month 7: Hailstones

Month 8: Locusts

Month 9: Darkness

[Month] 10: Death of the Firstborn-- however, this was not actually a month, as there was no further time for repentance offered. The plague occurred overnight, and then the Israelites were sent out.

If we look through the timeline in this way, we can count backwards through the months. Keeping in mind that the final plague was brought at the beginning of what would have been the 10th month, there is no timespan there to actually count (see this post for a review on tracking time). By this count, the plague of lice ended exactly 6 months before the exodus. 

An additional component: Thinking back to the explanation of R' Yaakov Ibn Chaviv, he explains that the Israelites were freed from work on Rosh Hashanah and freed from Egypt on Pesach. Based on our method for tracking time, does this work for counting the Jewish months from Rosh Hashanah to Pesach? Are there 6 months between the two holidays? (Remember, to count complete months!)