MySQL Non Sequential ID - mysql

Question

Challenge:
Create a method to set "auto_increment" values for tables in a non-sequential way.
The goal is to override the "auto_increment" mechanism and allow the function "LAST_INSERT_ID()" to continue working as expected (returning an INT), so that no changes are needed in software side.
My Solution
The method I found is based on an auxiliary table (unique_id), that stores values available to be assigned. Values are then selected randomly, and removed from the tables as used. When the table gets empty, a new set of ID's is created.
This example is working as expected, but with one problem.
Tables for the demo:
CREATE TABLE `unique_id` (
`id` INT(10) UNSIGNED NOT NULL AUTO_INCREMENT,
PRIMARY KEY (`id`)
)
COLLATE='latin1_swedish_ci'
ENGINE=InnoDB
AUTO_INCREMENT=100;
CREATE TABLE `test_unique_id` (
`id` INT(10) UNSIGNED NOT NULL AUTO_INCREMENT,
`name` VARCHAR(50) NOT NULL DEFAULT '0',
PRIMARY KEY (`id`)
)
COLLATE='latin1_swedish_ci'
ENGINE=InnoDB
AUTO_INCREMENT=1;
Defined a stored procedure and a function:
DELIMITER $$
DROP PROCEDURE IF EXISTS `UNIQUE_ID_REFILL`$$
CREATE PROCEDURE UNIQUE_ID_REFILL()
BEGIN
DECLARE a INT Default 0 ;
simple_loop: LOOP
SET a=a+1;
INSERT INTO unique_id (id) values(null);
IF a=100 THEN
LEAVE simple_loop;
END IF;
END LOOP simple_loop;
END $$
DROP FUNCTION IF EXISTS `UNIQUE_ID_GET`$$
CREATE FUNCTION UNIQUE_ID_GET()
RETURNS INT(11)
MODIFIES SQL DATA
BEGIN
DECLARE new_id INT(11);
DECLARE unique_id_count INT(11);
SET new_id = 0;
SELECT COUNT(*) INTO unique_id_count FROM unique_id;
IF unique_id_count=0 THEN
CALL UNIQUE_ID_REFILL();
END IF;
SELECT id INTO new_id FROM unique_id ORDER BY RAND() LIMIT 1;
DELETE FROM unique_id WHERE id = new_id;
RETURN new_id;
END $$
Created a Trigger on the destination table (test_unique_id):
CREATE TRIGGER test_unique_id__unique_id BEFORE INSERT ON test_unique_id
FOR EACH ROW
SET NEW.id = UNIQUE_ID_GET();
The solution is getting the random ID's as expected:
INSERT INTO test_unique_id(name) VALUES ('A'),('B'),('C');
Creates the rows:
id name
154 'A'
129 'B'
173 'C'
The Problem
The main problem is that LAST_INSERT_ID() stops working... and the software side is broken:
SELECT LAST_INSERT_ID();
0
Any ideas on how to solve this problem? or any other different approach to the challenge?
Thank you very much.