Cross-sectional variables in a time-series df with multiple imputation

Question

I have a dataset with time-series and cross-sectional variables with a sample size of less than 100. I have three variables (var1, var2, var3) that do not vary over time and a time-series variable (var4) that does vary over time.

I plan to examine associations between var1 and var2, var2 and var4, and var3 and var4. Before analysis, I want to conduct multiple imputation (mice). My <100 sample size and general research questions bar me from using SEM or path analysis, and therefore I don't believe FIML as a missing data treatment is an option for me.

If I wasn't conducting mice, I would examine var1 and var2 using a wide-form dataset, and examine other associations involving var4 with a long-form dataset. However, I believe it would be unwise to have more than one multiply-imputed dataset. Due to the variance inherent in mice, var2 will have different imputed values between the datasets. While I haven't read about this specific issue in the literature, it seems like a bad idea. Additionally, I want to avoid conducting analysis with var1 and var2 on a long-form dataset due to the variables' cross-sectional nature.

Is it possible to rectify both issues at the same time, or do I need to give in on one of them? If I have misunderstood anything, please correct me.

set.seed(1234)
library(tidyverse)
library(missMethods)
library(mice)

id <- rep(1:10)
var1 <- sample(1:10, 10, replace = TRUE)
var2 <- sample(1:20, 10, replace = TRUE)
var3 <- sample(10:30, 10, replace = TRUE)
wide <- data.frame(id, var1, var2, var3) %>%
  delete_MCAR(p = .2, cols_mis = c("var1", "var2", "var3"))

id <- rep(1:10, each = 10)
time <- rep(1:10, times = 10)
var4 <- rnorm(10)
long <- data.frame(id, time, var4) %>%
  delete_MCAR(p = .2, cols_mis = "var4")

df <- merge(wide, long, by = "id")

imputed_wide <- mice::mice(data = wide, m = 5, seed = 1234, 
                           printFlag = FALSE)
imputed_long <- mice::mice(data = df, m = 5, seed = 1234, 
                           printFlag = FALSE)

# Same analysis, different results on different data
summary(pool(with(data = imputed_wide, exp = lm(var1 ~ var2))))
#>          term    estimate std.error   statistic       df    p.value
#> 1 (Intercept)  6.19456035 1.9042540  3.25301157 3.969347 0.03163845
#> 2        var2 -0.01256283 0.1725381 -0.07281189 3.987911 0.94546139
summary(pool(with(data = imputed_long, exp = lm(var1 ~ var2))))
#>          term   estimate  std.error statistic       df      p.value
#> 1 (Intercept)  6.1510957 0.47795118 12.869716 93.92766 1.895427e-22
#> 2        var2 -0.0441173 0.04124086 -1.069747 95.42650 2.874315e-01

# Compare mean and SD of var2 between datasets
## Wide
impdat <- complete(imputed_wide, action = "long", include = FALSE)
pool_mean <- with(impdat, by(impdat, .imp, function(x) 
                     c(mean(x$var2), sd(x$var2))))
Reduce("+", pool_mean)/length(pool_mean)
#> [1] 9.380000 6.124072

## Long
impdat <- complete(imputed_long, action = "long", include = FALSE)
pool_mean <- with(impdat, by(impdat, .imp, function(x) 
                             c(mean(x$var2), sd(x$var2))))
Reduce("+", pool_mean)/length(pool_mean)
#> [1] 9.816000 6.076727