R Generate Bounded Random Sample Arround Specific Mean

I've been stuck with this for a while, so I decided to write a question.

Problem: How to generate a random sample (of lenght n) with a lower/upper bound and arround a specific mean.

Observation: distribution doesn't need to be specific (it could be normal, beta, etc).

Aproaches considered:

• One aproach is to use the rtnorm function (package msm) which generates a random numbers with a normal distribution within specified bounds but it doesn't hold your wanted mean value.

• A second aproach I've tried is this function which I found in a question I can't find anymore

  rBootstrap<-function(n,mean,sd,lowerBound,upperBound){
    range <- upperBound - lowerBound
    m <- (mean-lowerBound) / range #mapping mean to 0-1 range
    s <- sd / range #mapping sd to 0-1 range
    a <- (m^2 - m^3 - m*s^2)/s^2 #calculating alpha for rbeta 
    b <- (m-2*m^2+m^3-s^2+m*s^2)/s^2 #calculating beta for rbeta
    data <- rbeta(n,a,b)  #generating data
    data <- lowerBound + data * range #remaping to given bounds
    return(data)
  }
  
  

  this function actually gives great results unless: upperBound > lowerBound + (2* mean - lowerBound) (upper bound exceeds two times the distance from the lowerBound to the mean).

Particularly, I would like to generate a random sample of lenght 1,800, with values between 50,000 and 250,000 with mean value = 70,000.