Create grouping based on cumulative sum and another group

This question is nearly identical to: Create new group based on cumulative sum and group

However, when I apply the accepted solution to my data, it doesn't have the expected result.

In a nutshell, I have a data with two variables: domain and value. Domain is a group variable with multiple observations and value is some continuous value that I would like to accumulate by domain and great a new group variable, newgroup. There are three main rules:

1. I accumulate only within each domain. If I reach the end of the domain, then the accumulation is reset.
2. If the accumulated sum is at least 1.0 then the observations whose values added up to at least 1.0 are assigned to a different value for group1. Please note that this rule can be satisfied by a single observation.
3. If the last group in a domain has an accumulated sum less than 1.0, then merge that with the second to last group within the same domain. This is reflected in the variable group2

The data below has been simplified. The data will usually consist of 10^5 - 10^6 rows, so a vectorized solution would be ideal.

Example Data

domain <- c(rep(1,5),rep(2,8))
value <- c(1,0,2,2.5,0.1,0.1,0.5,0,0.2,0.6,0,0,0.1)
df_raw <- data.frame(domain,value)


 domain value
      1   1.0
      1   0.0
      1   2.0
      1   2.5
      1   0.1
      2   0.1
      2   0.5
      2   0.0
      2   0.2
      2   0.6
      2   0.0
      2   0.0
      2   0.1

Desired Output

cumsum_val <- c(1,0,2,2.5,0.1,0.1,0.6,0.6,0.8,1.4,0,0,0.1)
group1 <- c(1,2,2,3,4,5,5,5,5,5,6,6,6)
group2 <- c(1,2,2,3,3,4,4,4,4,4,4,4,4) #Satisfies Rule #3
df_want <- data.frame(domain,value,cumsum_val,group1,group2)

 domain value cumsum_val group1 group2
      1   1.0        1.0      1      1
      1   0.0        0.0      2      2
      1   2.0        2.0      2      2
      1   2.5        2.5      3      3
      1   0.1        0.1      4      3
      2   0.1        0.1      5      4
      2   0.5        0.6      5      4
      2   0.0        0.6      5      4
      2   0.2        0.8      5      4
      2   0.6        1.4      5      4
      2   0.0        0.0      6      4
      2   0.0        0.0      6      4
      2   0.1        0.1      6      4

I used the following code:

sum0 <- function(x, y) { if (x + y >= 1.0) 0 else x + y }
is_start <- function(x) head(c(TRUE, Reduce(sum0, init=0, x, acc = TRUE)[-1] == 0), -1)
cumsum(ave(df_raw$value, df_raw$domain, FUN = is_start))
## 1 2 3 4 5 6 6 6 6 6 7 8 9

but the last line does not produce the same values as group1 above. Generating group1 output is what is mainly causing me issues. Can someone help me understand the function is_start and how that is supposed to produce the groupings?

EDITakrun provided some working code in the comments for the simplified example above. However, there are still some situations where it doesn't work. For example,

domain <- c(rep(1,7),rep(2,8))
value <- c(1,0,1,0,2,2.5,0.1,0.1,0.5,0,0.2,0.6,0,0,0.1)
df_raw <- data.frame(domain,value)

The output is show below with new coming from akrun's code and group1 and group2 are the desired groupings based on rules #2 and #3. The discrepancy between new and group2 occurs mainly in the first 3 rows.

 domain value new group1 group2
      1   1.0   1      1      1
      1   0.0   2      2      2
      1   1.0   3      2      2
      1   0.0   4      3      3
      1   2.0   4      3      3
      1   2.5   5      4      4
      1   0.1   5      5      4
      2   0.1   6      6      5
      2   0.5   6      6      5
      2   0.0   6      6      5
      2   0.2   6      6      5
      2   0.6   6      6      5
      2   0.0   6      7      5
      2   0.0   6      7      5
      2   0.1   6      7      5